Turbulent flow between concentric cylinders is studied in experiments for Reynolds numbers 800
Lee.PRL.2003
Observation of Anomalous Momentum Transport in Tokamak Plasmas with No Momentum Input
Lee and Rice and Marmar and Greenwald and Hutchinson and Snipes
prl
91
205003
(2003)
Lehnert.AF.1952
On the behaviour of an electrically--conducting liquid in a magnetic field
Lehnert
af
5
69
(1952)
Lehnert.AF.1957
An experiment on axisymmetric flow of liquid sodium in a magnetic field
Lehnert
af
13
109--116
(1957)
Lehnert.PR.1954
Magneto-Hydrodynamic Waves in Liquid Sodium
Lehnert
Phys. Rev.
94
(1954)
Magneto-Hydrodynamic Waves in Liquid Sodium.pdf
http://link.aps.org/abstract/PR/v94/p815
Liquid sodium, because of its higher electrical conductivity and lower density, is more suitable than mercury for magneto-hydrodynamic experiments. Torsional waves in liquid sodium have been generated in a cylindrical vessel with the axis parallel to a homogeneous magnetic field, and resonance phenomena have been investigated at constant frequency and variable magnetic field strength. The agreement between theory and experiment is satisfactory. It is shown that even with sodium, damping plays an important role under laboratory conditions. The calculations of this paper are also used to improve the results of earlier investigations with mercury.
Leorat.JFM.1981
{Fully developed MHD turbulence near critical magnetic Reynolds number}
{L\'eorat} and {Pouquet} and {Frisch}
jfm
104
419-443
(1981)
Fully developed MHD turbulence near critical.pdf
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1981JFM...104..419L&db_key=PHY
Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.
This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.
We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L [approximate] l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.
We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).
Leprovost.AJ.2007
Effect of Rossby and Alfv\'en Waves on the Dynamics of the Tachocline
Leprovost and Kim
The Astrophysical Journal
654
1166--1170
(2007)
Effect of Rossby and Alfv\'en Waves on the Dynamics.pdf
10.1086/509713
To understand magnetic diffusion, momentum transport, and mixing in the interior of the Sun, we consider an idealized model of the tachocline, namely, magnetohydrodynamic (MHD) turbulence on a b-plane subject to a large-scale shear (provided by the latitudinal differential rotation). This model enables us to self-consistently derive the influence of shear, Rossby, and Alfven waves on the transport properties of turbulence. In the strong magnetic field regime, we find that the turbulent viscosity and diffusivity are reduced by magnetic fields only, as in the two-dimensional MHD case (without Rossby waves). In the weak magnetic field regime, we find a crossover scale (LR) from a Alfven-dominated regime (on small scales) to a Rossby-dominated regime (on large scales). For parameter values typical of the tachocline, LR is larger than the solar radius so that Rossby waves are unlikely to play an important role in the transport of magnetic field and angular momentum. This is mainly due to the enhancement of magnetic back-reaction by shearing, which efficiently generates small scales, and thus strong currents.
Leprovost.EPJB.2005
The turbulent dynamo as an instability in a noisy medium
Leprovost and Dubrulle
epjb
44
395--400
(2005)
10.1140/epjb/e2005-00138-y
Leprovost.PRE.2006
Dynamics and thermodynamics of axisymmetric flows: Theory
Leprovost and Dubrulle and Chavanis
pre
73
046308
(2006)
Lesur.AA.2005
On the relevance of subcritical hydrodynamic turbulence to accretion disk transport
{G.Lesur} and {P.-Y.Longaretti}
Astron. Astrophys.
444
25-44
(2005)
On the relevance of subcritical hydrodynamic turbulence to accretion.pdf
http://dx.doi.org/doi/10.1051/0004-6361:20053683
10.1051/0004-6361:20053683
Hydrodynamic unstratified Keplerian flows are known to be linearly stable at all Reynolds numbers, but may nevertheless become turbulent through nonlinear mechanisms. However, in the last ten years, conflicting points of view have appeared on this issue. We have revisited the problem through numerical simulations in the shearing sheet limit. It turns out that the effect of the Coriolis force in stabilizing the flow depends on whether the flow is cyclonic (cooperating shear and rotation vorticities) or anticyclonic (competing shear and rotation vorticities); Keplerian flows are anticyclonic. We have obtained the following results:
i/ The Coriolis force does not quench turbulence in subcritical flows; however, turbulence is more efficient, and much more easily found, in cyclonic flows than in anticyclonic ones.
ii/ The Reynolds number/rotation/resolution relation has been quantified in this problem. In particular we find that the resolution demand, when moving away from the marginal stability boundary, is much more severe for anticyclonic flows than for cyclonic ones. Presently available computer resources do not allow numerical codes to reach the Keplerian regime.
iii/ The efficiency of turbulent transport is directly correlated to the Reynolds number of transition to turbulence Rg, in such a way that the Shakura-Sunyaev parameter $\alpha\sim 1/Rg$. This correlation is nearly independent of the flow cyclonicity. The correlation is expected on the basis of generic physical arguments.
iv/ Even the most optimistic extrapolations of our numerical data show that subcritical turbulent transport would be too inefficient in Keplerian flows by several orders of magnitude for astrophysical purposes. Vertical boundary conditions may play a role in this issue although no significant effect was found in our preliminary tests.
v/ Our results suggest that the data obtained for Keplerian-like flows in a Taylor-Couette settings are largely affected by secondary flows, such as Ekman circulation.
Lewis.PR.1999
Velocity structure functions, scaling, and transitions in high-Reynolds-number Couette-Taylor flow
Lewis and Swinney
Phys. Rev. E
59
(1999)
Velocity structure functions, scaling, and transitions.pdf
http://link.aps.org/abstract/PRE/v59/p5457
Li.AJ.2000
Rossby Wave Instability of Thin Accretion Disks. II. Detailed Linear Theory
Li and Finn and Lovelace and Colgate
Astro. Phys. J.
533
1023--1034
(2000)
Rossby Wave Instability of Thin Accretion.pdf
http://dx.doi.org/10.1086/308693
10.1086/308693
In an earlier work we identified a global, nonaxisymmetric instability associated with the presence of an extreme in the radial profile of the key function {\$}{$\backslash$}mathstrut{\{}{$\backslash$}cal L{\}} ( r) {$\backslash$}equiv ( {$\backslash$}Sigma {$\backslash$}Omega / {$\backslash$}kappa \^{}{\{}2{\}}) S\^{}{\{}2/ {$\backslash$}Gamma {\}}{\$} in a thin, inviscid, nonmagnetized accretion disk. Here {\$}{$\backslash$}Sigma ( r) {\$} is the surface mass density of the disk, {\$}{$\backslash$}Omega ( r) {\$} is the angular rotation rate, {\$}S( r) {\$} is the specific entropy, Γis the adiabatic index, and {\$}{$\backslash$}kappa ( r) {\$} is the radial epicyclic frequency. The dispersion relation of the instability was shown to be similar to that of Rossby waves in planetary atmospheres. In this paper, we present the detailed linear theory of this Rossby wave instability and show that it exists for a wider range of conditions, specifically, for the case where there is a ``jump''over some range of r in {\$}{$\backslash$}Sigma ( r) {\$} or in the pressure {\$}P( r) {\$} . We elucidate the physical mechanism of this instability and its dependence on various parameters, including the magnitude of the ``bump''or ``jump,''the azimuthal mode number, and the sound speed in the disk. We find a large parameter range where the disk is stable to axisymmetric perturbations but unstable to the nonaxisymmetric Rossby waves. We find that growth rates of the Rossby wave instability can be high, ∼{\$}0.2{$\backslash$}Omega {\_}{\{}{$\backslash$}mathrm{\{}K{\}}{$\backslash$},{\}}{\$} for relative small jumps or bumps. We discuss possible conditions which can lead to this instability and the consequences of the instability.
Li.AJ.2001
Rossby Wave Instability of Thin Accretion Disks. III. Nonlinear Simulations
Li and Colgate and Wendroff and Liska
Astro. Phys. J.
551
874--896
(2001)
Rossby Wave Instability of Thin Accretion0.pdf
http://dx.doi.org/10.1086/320241
10.1086/320241
We study the nonlinear evolution of the Rossby wave instability in thin disks using global two‐dimensional hydrodynamic simulations. The detailed linear theory of this nonaxisymmetric instability was developed earlier by Lovelace et al. and Li et al., who found that the instability can be excited when there is an extremum in the radial profile of an entropy‐modified version of potential vorticity. The key questions we are addressing in this paper are the following: (1) What happens when the instability becomes nonlinear? Specifically, does it lead to vortex formation? (2) What is the detailed behavior of a vortex? (3) Can the instability sustain itself and can the vortex last a long time? Among various initial equilibria that we have examined, we generally find that there are three stages of the disk evolution: (1) The exponential growth of the initial small amplitude perturbations. This is in excellent agreement with the linear theory; (2) The production of large‐scale vortices and their interactions with the background flow, including shocks. Significant accretion is observed owing to these vortices. (3) The coupling of Rossby waves/vortices with global spiral waves, which facilitates further accretion throughout the whole disk. Even after more than 20 revolutions at the radius of vortices, we find that the disk maintains a state that is populated with vortices, shocks, spiral waves/shocks, all of which transport angular momentum outward. We elucidate the physics at each stage and show that there is an efficient outward angular momentum transport in stages (2) and (3) over most parts of the disk, with an equivalent Shakura‐Sunyaev angular momentum transport parameter αin the range from 10−4 to 10−2. By carefully analyzing the flow structure around a vortex, we show why such vortices prove to be almost ideal ``units''in transporting angular momentum outward, namely by positively correlating the radial and azimuthal velocity components. In converting the gravitational energy to the internal energy, we find some special cases in which entropy can remain the same while angular momentum is transported. This is different from the classical α‐disk model, which results in the maximum dissipation (or entropy production). The dependence of the transport efficiency on various physical parameters are examined and effects of radiative cooling are briefly discussed as well. We conclude that Rossby wave/vortex instability is an efficient, purely hydrodynamic mechanism for angular momentum transport in thin disks, and may find important applications in many astrophysical systems.
Lilley.PRSLA.1970
On Kinemtic Dynamos
Lilley
prsla
316
153--167
(1970)
http://links.jstor.org/sici?sici=0080-4630%2819700414%29316%3A1525%3C153%3AOKD%3E2.0.CO%3B2-0
Liu.AJ.2008
Numerical Study of the Magnetorotational Instability in Princeton MRI Experiment
Liu
Astrophys. J.
684
515-524
(2008)
Numerical Study of the Magnetorotational Instability in Princeton.pdf
http://www.journals.uchicago.edu/doi/abs/10.1086/590366
In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we present nonideal axisymmetric magnetohydrodynamic simulations of the nonlinear evolution of MRI in the experimental geometry. The simulations adopt fully insulating boundary conditions. No-slip conditions are imposed at all boundaries. A clear linear phase is observed with reduced linear growth rate. MRI results in an inflowing jet near the midplane and enhances the angular momentum transport at saturation.
Liu.APJ.2006
Simulations of Magnetorotational Instability in a Magnetized Couette Flow
Liu and Goodman and Ji
Astro. Phys. J.
643
306--317
(2006)
Simulations of Magnetorotational Instability in a Magnetized Couette0.pdf
http://dx.doi.org/10.1086/501495
In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we present nonideal two‐dimensional magnetohydrodynamic simulations of the nonlinear evolution of MRI in the experimental geometry. The simulations adopt initially uniform vertical magnetic fields, conducting radial boundaries, and periodic vertical boundary conditions. No‐slip conditions are imposed at the cylinders. Our linear growth rates compare well with existing local and global linear analyses. The MRI saturates nonlinearly with horizontal magnetic fields comparable to the initial axial field. The rate of angular momentum transport increases modestly but significantly over the initial state. For modest fluid and magnetic Reynolds numbers {\$}{$\backslash$}mathrm{\{}Re{\}}{$\backslash$},,{$\backslash$}mathrm{\{}Re{\}}{$\backslash$},{\_}{\{}m{\}}{$\backslash$}sim 10\^{}{\{}2{\}}{\{}{$\backslash$}mbox{\{}--{\}}{\}} 10\^{}{\{}3{\}}{\$} , the final state is laminar reduced mean shear except near the radial boundaries, and with poloidal circulation scaling as the square root of resistivity, in partial agreement with the analysis of Knobloch and Julien. A sequence of simulations at {\$}{$\backslash$}mathrm{\{}Re{\}}{$\backslash$},{\_}{\{}m{\}}=20{\$} and {\$}10\^{}{\{}2{\}}{$\backslash$}lesssim {$\backslash$}mathrm{\{}Re{\}}{$\backslash$},{$\backslash$}lesssim 10\^{}{\{}4.4{\}}{\$} enables extrapolation to the experimental regime ( {\$}{$\backslash$}mathrm{\{}Re{\}}{$\backslash$},{\_}{\{}m{\}}{$\backslash$}approx 20{\$} , {\$}{$\backslash$}mathrm{\{}Re{\}}{$\backslash$},{$\backslash$}sim 10\^{}{\{}7{\}}{\$} ), albeit with unrealistic boundary conditions. MRI should increase the experimentally measured torque substantially over its initial purely hydrodynamic value.
Liu.FEPEC.2007
{Liquid metal cooling in thermal management of computer chips}
Liu and Ma
Frontiers of Energy and Power Engineering in China
1
384--402
(2007)
Liu.PRE.2006
Helical magnetorotational instability in magnetized Taylor-Couette flow
Liu and Goodman and Herron and Ji
Phys. Rev. E
74
056302--8
(2006)
Helical magnetorotational instability in magnetized Taylor-Couette.pdf
http://link.aps.org/abstract/PRE/v74/e056302
Liu.PRE.2007
Traveling waves in a magnetized Taylor-Couette flow
Liu and Goodman and Ji
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
76
016310--4
(2007)
Traveling waves in a magnetized Taylor-Couette flow.pdf
http://link.aps.org/abstract/PRE/v76/e016310
We investigate numerically a traveling wave pattern observed in experimental magnetized Taylor-Couette flow at low magnetic Reynolds number. By accurately modeling viscous and magnetic boundaries in all directions, we reproduce the experimentally measured wave patterns and their amplitudes. Contrary to previous claims, the waves are shown to be transiently amplified disturbances launched by viscous boundary layers, rather than globally unstable magnetorotational modes.
Liu.PRE.2008
Magnetized Ekman layer and Stewartson layer in a magnetized Taylor-Couette flow
Liu
Phys. Rev. E
77
056314--11
(2008)
Magnetized Ekman layer and Stewartson layer.pdf
http://link.aps.org/abstract/PRE/v77/e056314
Liu.Thesis.2007
Axisymmetric Numerical and Analytical Studies of the Magnetorotational Instability in a Magnetized Taylor-Couette Flow
Liu
(2007)
Axisymmetric Numerical and Analytical Studies of the Magnetorotational.pdf
http://mri.pppl.gov/Wei-thesis.pdf
The magnetorotational instability (MRI) is probably the main cause of
turbulence and accretion in sufficiently ionized astrophysical disks.
However, despite much theoretical and computational work, the nonlinear
saturation of MRI is imperfectly understood. In this thesis we present non-ideal
magnetohydrodynamic simulations of the Princeton MRI
experiment. In vertically infinite or periodic cylinders, MRI saturates in a resistive current-sheet with
significant reduction of the mean shear, and with poloidal circulation scaling
as the square root of resistivity. Angular momentum transport scales
as the reciprocal square root of viscosity but only weakly depends on
resistivity. For finite cylinders with insulating end caps, a method for
implementing full insulating boundary condition is introduced. MRI grows with a clear linear phase
from small amplitudes at rates in good agreement
with linear analysis. In the final state
one inflowing ``jet" opposite to the usual Ekman ``jet" is found
near the inner cylinder. The MRI enhances the angular momentum transport at saturation. Under proper condition our experimental facility is a good platform to show that MRI could be suppressed by a strong magnetic field.
Recently, Hollerbach and R\"{u}diger have reported that MRI modes may grow at much
reduced magnetic Reynolds number $(\Rm)$ and Lundquist number $S$ in the presence of a helical background field, a
current-free combination of axial and toroidal
field. We have investigated these helical MRI
modes. In vertically infinite or periodic cylinders, resistive HMRI is a
weakly destabilized hydrodynamic inertial oscillation propagating axially along
the background Poynting flux. Growth rates are small, however, and require large
axial currents. Furthermore, finite cylinders with insulating endcaps were shown
to reduce the growth rate and to stabilize highly resistive, inviscid flows entirely, and the new mode is stable in Keplerian flow profiles
regardless of end conditions. We also numerically investigate a traveling wave
pattern observed in experimental magnetized Taylor-Couette flow at low magnetic
Reynolds number. By accurately modeling viscous and magnetic boundaries in all
directions, we reproduce the experimentally measured wave patterns and their
amplitudes. Contrary to previous claims, the waves are shown to be transiently
amplified disturbances launched by viscous boundary layers rather than globally
unstable magnetorotational modes.
The experiment is complicated by the extremely large Reynolds number and by
Ekman circulation and Stewartson layers, even though the
experimental apparatus has been designed to minimize the circulation (\emph{e.g.} by the use of independently controlled split
endcaps). Understanding the role of
the boundary layer is critical to this research. The magnetic field is found to inhibit the Ekman suction. While we quantitatively confirmed the conclusions of Gilman \emph{et al}, the finite differential rotation cannot be neglected and modifies the linear Ekman layer. The width of the Ekman layer is reduced with increased magnetic field normal to the end plate. A uniformly-rotating region forms near the outer cylinder. The Stewartson layer penetrates deeper into the fluid with larger Reynolds number and stronger magnetic field. Furthermore a strong magnetic field leads to a steady Stewartson layer, at least in axisymmetry.
Livermore.PRSLA.2004
On magnetic energy instability in spherical stationary flows
Livermore and Jackson
Proc. R. Soc. Lond. A
460
1453--1476
(2004)
Livio-APJ-1988
{Nova outbursts on magnetic white dwarfs}
{Livio} and {Shankar} and {Truran}
Astrophys. J.
330
264-273
(1988)
Nova outbursts on magnetic white dwarfs.pdf
10.1086/166470
The question of nova outbursts on magnetic white dwarfs among AM Her systems is examined. In particular, the effects of the presence of a strong magnetic field on the development of a thermonuclear runaway (TNR) are studied. The magnetic field is capable of weakening the outburst both through the inhibition of shear and diffusion mixing (which results in lower enrichments by heavy elements) and by interference with the development of convection during the TNR (which results in lower ejection velocities). The apparent absence of classical novae among AM Her systems may nevertheless have been due to selection effects, which are a consequence of the lower accretion rates below the period gap and the very narrow range in mass ratios capable of producing novae below the gap.
Livio.ASPCS.1995
{Nova Outbursts on Magnetic White Dwarfs}
{Livio}
85
80--88
(1995)
Nova Outbursts on Magnetic White Dwarfs0.pdf
Lomb.SS.1976
Least-squares frequency analysis of unequally spaced data Astrophys
Lomb
Space Sci
39
447--462
(1976)
Least-squares frequency analysis of unequally spaced.pdf
The statistical properties of least-squares frequency analysis of unequally spaced data are
examined. It is shown that, in the least-squares spectrum of gaussian noise, the reduction in the sum of
squares at a particular frequency is a Z2 2 variable. The reductions at different frequencies are not
independent, as there is a correlation between the height of the spectrum at any two frequencies, fl
and f2, which is equal to the mean height of the spectrum due to a sinusoidal signal of frequency fl,
at the frequency f2. These correlations reduce the distortion in the spectrum of a signal affected by
noise. Some numerical illustrations of the properties of least-squares frequency spectra are also
given.
London.GAFD.2005
Resistive wave breaking in the Earth's outer core.
London
Geophys. Astrophys. Fluid Dynamics
99
397--411
(2005)
Resistive wave breaking in the Earth's outer.pdf
http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=19063419&site=ehost-live
10.1080/03091920500304541
The equations for an electrically conducting fluid in cylindrical coordinates are linearized assuming that the inertial terms in the momentum equation can be ignored (small Rossby number), and that the ratio of the Elsasser number and magnetic Reynolds number is one. After these assumptions, the governing equations are linearized about an ambient solution which vanishes at the the equator. Upon assuming large Elsasser and magnetic Reynolds number, the solutions to the linearized equations are approximated by wave trains having very short wave length (relative to the core radius) but which vary slowly (on a scale of the core radius). The period of the waves is much longer than a day but much shorter than the period of the slow hydromagnetic oscillations. These waves are found to be trapped in a region about the equator and away from the axis of rotation. The waves break at a latitudinal wave region boundary, in the sense that the waves become exponentially large in a boundary layer, having as an exponent some positive power of the large azimuthal wave number. This behavior is amplified as the Elsasser number becomes smaller while still remaining relatively large. Waves in more Earth-like parameter regimes are discussed briefly.
Longo.EF.2006
{The effects of air bubbles on ultrasound velocity measurements}
Longo
Exp. Fluids
41
593--602
(2006)
Love.AG.2005
Love
ag
40
6.14--6.19
(1999)
Lovelace.AJ.1999
Rossby Wave Instability of Keplerian Accretion Disks
Lovelace and Li and Colgate and Nelson
Astro. Phys. J.
513
805--810
(1999)
Rossby Wave Instability of Keplerian Accretion.pdf
http://dx.doi.org/10.1086/306900
We find a linear instability of nonaxisymmetric Rossby waves in a thin nonmagnetized Keplerian disk when there is a local maximum in the radial profile of a key function {\$}{$\backslash$}mathstrut{\{}{$\backslash$}cal L{\}} ( r) {$\backslash$}equiv {$\backslash$}mathstrut{\{}{$\backslash$}cal F{\}} ( r) S\^{}{\{}2/ {$\backslash$}Gamma {\}}( r) {\$} , where {\$}{$\backslash$}mathstrut{\{}{$\backslash$}cal F{\}} \^{}{\{}-1{\}}={$\backslash$}hat{\{}{$\backslash$}boldsymbol{\{}z{\}}{\}}{\{}{$\backslash$}mbox{\{}{$\backslash$}boldmath{\$}{$\backslash$}cdot{\$}{\}}{\}} ( {\{}{$\backslash$}mbox{\{}{$\backslash$}boldmath{\$}{$\backslash$}nabla{\$}{\}}{\}} {$\backslash$}mbox{\{}{$\backslash$}boldmath{\$}{$\backslash$}times{\$}{\}} {$\backslash$}boldsymbol{\{}v{\}}) / {$\backslash$}Sigma {\$} is the potential vorticity, {\$}S=P/ {$\backslash$}Sigma \^{}{\{}{$\backslash$}Gamma {\}}{\$} is the entropy, Σis the surface mass density, P is the vertically integrated pressure, and Γis the adiabatic index. We consider in detail the special case where there is a local maximum in the disk entropy profile {\$}S( r) {\$} . This maximum acts to trap the waves in its vicinity if its height‐to‐width ratio {\$}{$\backslash$}mathrm{\{}max{\}}{$\backslash$},( S) / {$\backslash$}Delta r{\$} is larger than a threshold value. The pressure gradient derived from this entropy variation provides the restoring force for the wave growth. We show that the trapped waves act to transport angular momentum outward. A plausible way to produce an entropy variation is when an accretion disk is starting from negligible mass and temperature, therefore, negligible entropy. As mass accumulates by either tidal torquing, magnetic torquing, or Roche‐lobe overflow, confinement of heat will lead to an entropy maximum at the outer boundary of the disk. Possible nonlinear developments from this instability include the formation of Rossby vortices and the formation of spiral shocks. What remains to be determined from hydrodynamic simulations is whether or not Rossby wave packets (or vortices) ``hold together''as they propagate radially inward.
Lowes.Nature.1963
Geomagnetic Dynamo: A Laboratory Model
Lowes and Wilkinson
nature
198
1158--1160
(1963)
Lowes.Nature.1968
Geomagnetic Dynamo: An Improved Laboratory Model
Lowes and Wilkinson
nature
219
717--718
(1968)
Lundquist.PR.1949
Experimental Investigations of Magneto-Hydrodynamic Waves
Lundquist
Phys. Rev.
76
(1949)
Experimental Investigations of Magneto-Hydrodynamic Waves.pdf
http://link.aps.org/abstract/PR/v76/p1805
The importance of magneto-hydrodynamic phenomena to different parts of cosmic physics is becoming more and more evident. This fact and the extreme mathematical difficulties involved in an exact treatment of many problems make it necessary to consider the possibility for experimental investigations. In this paper the fundamental equations are solved for cylindrically limited waves, a case which seems to be best adapted for experiments. It is shown that an "ideal" magneto-hydrodynamic wave in a liquid with finite conductivity can exist only in a certain frequency interval. The upper limit is set by the conductivity and the magnetic field strength. Above this value the waves degenerate into skin-waves. The lowest frequency is determined by the geometrical dimensions and by the conductivity. Waves in different liquids are compared, and liquid sodium is found to be the best medium for an experiment. A brief account is given for a preliminary experiment and other investigations are proposed.
Lvov.PRE.1999
{Temporal surrogates of spatial turbulent statistics: The Taylor hypothesis revisited}
L'vov and Pomyalov and Procaccia
pre
60
4175-4184
(1999)
http://link.aps.org/abstract/PRE/v60/p4175
MILES.JFM.1993
SURFACE-WAVE GENERATION REVISITED
MILES
J. Fluid Mech.
256
427-441
(1993)
SURFACE-WAVE GENERATION REVISITED1.pdf
10.1017/S0022112093002836
The quasi-laminar model for the transfer of energy to a surface wave from a turbulent shear flow (Miles 1957) is modified to incorporate the wave-induced perturbations of the Reynolds stresses, which are related to the wave-induced velocity field through the Boussinesq closure hypothesis and the ancillary hypothesis that the eddy viscosity is conserved along streamlines. It is assumed that the basic mean velocity is U(Z) = (U*/kappa) log (z/z0) for sufficiently large z (elevation above the level interface) and that U(z1) much greater than U* for kz1 = O(1), where k is the wavenumber. The resulting vorticity-transport equation is reduced, through the neglect of diffusion, to a modification of Rayleigh's equation for wave motion in an inviscid shear flow. The energy transfer to the surface wave, which comprises independent contributions from the critical layer (where U = c, the wave speed) and the wave-induced Reynolds stresses, is calculated through a variational approximation and, independently, through matched asymptotic expansions. The critical-layer component is equivalent to that for the quasi-laminar model. The Reynolds-stress component is similar to, but differs quantitatively from, that obtained by Knight (1977), Jacobs (1987) and van Duin \& Janssen (1992). The predicted energy transfer agrees with the observational data compiled by Plant (1982) for 1 less than or similar to c/U* less than or similar to 20, but the validity of the logarithmic profile for the calculation of the energy transfer in the critical layer for c/U* < 5 remains uncertain. The basic model is unreliable (for water waves) if c/U* less-than-or-similar-to 1, but this domain is of limited oceanographic importance. It is suggested that Kelvin-Helmholtz instability of air blowing over oil should provide a good experimental test of the present Reynolds-stress modelling and that this modelling may be relevant in other geophysical contexts.
Mallock.PRSL.1888
Determination of the Viscosity of Water
Mallock
prsl
45
126--132
(1888)
Malmberg.PP.2004
Mode and plasma rotation in a resistive shell reversed--field pinch
Malmberg and Brzozowski and Brunsell and Cecconello and Drake
pp
11
647--658
(2004)
Marie.EPJB.2003
{Numerical study of homogeneous dynamo based on experimental von K\'arm\'an type flows}
Mari\'e and Burguete and Daviaud and L\'eorat
epjb
33
469--485
(2003)
http://publish.edpsciences.com/articles/epjb/abs/2003/12/b02780/b02780.html
Marie.PF.2006
{Galerkin analysis of kinematic dynamos in the von K\'arm\'an geometry}
Mari\'e and Normand and Daviaud
pf
18
017102
(2006)
http://link.aip.org/link/?PHF/18/017102/1
Marquardt.JSIAM.1963
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
Marquardt
jsiam
11
431--441
(1963)
Martin.EPJB.2000
Magnetic permeability of a diphasic flow, made of liquid gallium and iron beads
Martin and Odier and Pinton and Fauve
epjb
18
337--341
(2000)
Masada:2007aa
The Effect of Neutrino Radiation on Magnetorotational Instability in Proto-Neutron Stars
Masada and Sano and Shibata
The Astrophysical Journal
655
447-457
(2007)
The Effect of Neutrino Radiation on Magnetorotational Instability.pdf
http://www.journals.uchicago.edu/doi/abs/10.1086/509799
Neutrino radiation takes a major role in the momentum, heat, and lepton transports in proto-neutron stars (PNSs). These diffusive processes affect the growth of the magnetorotational instability (MRI) in PNSs. We perform a local linear analysis for the axisymmetric and nonaxisymmetric MRI including the effects of neutrino transport and ohmic dissipation. We find that the MRI can grow even in the multidiffusive situations that are realized in neutrino-loaded PNSs. When the toroidal magnetic component dominates over the poloidal one, nonaxisymmetric MRI modes grow much faster than axisymmetric modes. These results suggest the importance of the nonaxisymmetric MRI in PNSs. Thus, understanding the three-dimensional nonlinear evolution of the MRI is necessary for revealing the explosion mechanism of core-collapse supernovae.
Matisse.PF.1984
Neutrally buoyant anisotropic particles for flow visualization
Matisse and Gorman
Phys. Fluids
27
759--760
(1984)
Neutrally buoyant anisotropic particles for flow.pdf
http://link.aip.org/link/?PFL/27/759/1
Anisotropic flakes dispersed in certain liquids are shown to remain suspended for periods of the order of months. Such particles represent an ideal flow visualization technique, especially for thermally driven flows such as Rayleigh--Bénard convection.
Matsumoto.AJ.1995
Magnetic viscosity by localized shear flow instability in magnetized accretion disks
Matsumoto and Tajima
aj
445
767--779
()
Mattas.FED.2000
ALPS-advanced limiter-divertor plasma-facing systems
Mattas and Allain and Bastasz and Brooks and Evans and Hassanein and Luckhardt and McCarthy and Mioduszewski and Maingi and Mogahed and Moir and Molokov and Morely and Nygren and Rognlien and Reed and Ruzic and Sviatoslavsky and Sze and Tillack and Ulrickson and Wade and Wooley and Wong
Fusion Engineering and Design
49-50
127--134
(2000)
ALPS-advanced limiter-divertor plasma-facing systems.pdf
http://www.sciencedirect.com/science/article/B6V3C-424THNY-J/1/c7922f5545df068e989acad144c65b2d
The advanced limiter-divertor plasma-facing systems (ALPS) program was initiated in order to evaluate the potential for improved performance and lifetime for plasma-facing systems. The main goal of the program is to demonstrate the advantages of advanced limiter/divertor systems over conventional systems in terms of power density capability, component lifetime, and power conversion efficiency, while providing for safe operation and minimizing impurity concerns for the plasma. Most of the work to date has been applied to free surface liquids. A multi-disciplinary team from several institutions has been organized to address the key issues associated with these systems. The main performance goals for advanced limiters and divertors are a peak heat flux of >50 MW/m2, elimination of a lifetime limit for erosion, and the ability to extract useful heat at high power conversion efficiency (~40%). The evaluation of various options is being conducted through a combination of laboratory experiments, modeling of key processes, and conceptual design studies. The current emphasis for the work is on the effects of free surface liquids on plasma edge performance.
Mattor.PF.1988
Momentum and thermal transport in neutral-beam-heated tokamaks
Mattor and Diamond
pf
31
1180--1189
(1988)
May.N.1976
Simple mathematical models with very complicated dynamics
May
Nature
261
459--467
(1976)
Simple mathematical models with very.pdf
http://dx.doi.org/10.1038/261459a0
First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.
McEwan.JFM.1970
Inertial oscillations in a rotating fluid cylinder
McEwan
J. Fluid Mech.
40
603--640
(1970)
Inertial oscillations in a rotating fluid cylinder.pdf
10.1017/S0022112070000344
A study is described of the forced inertial oscillations appearing in an axially rotating completely filled circular cylinder with plane ends. Excitation is provided by causing the top end to rotate about an axis inclined slightly to the rotation axis. Experiments demonstrate the presence of numerous low mode resonances in a densely spaced range of ratios of net cylinder height to radius in close conformance with linear inviscid theory. Where geometry permits simple corner reflexion, characteristic surfaces are revealed which confirm in part the theoretical predictions concerning their scale and form.
Detailed measurements are given of the amplitude at one point within the cylinder for the condition in which the disturbance frequency equals the rotation frequency. Amplitude column height spectra are compared with theoretical estimates, and the evolution of amplitude for the simplest mode of resonant oscillation is studied. A non-linear theory based on the integral energy of large amplitude oscillation is derived whose broad features are in fair quantitative and qualitative agreement with these observations.
Some investigation is made of the phenomenon of resonant collapse, in which larger amplitude resonant oscillations, after persisting in an apparently laminar form, degenerate abruptly into a state of agitation and disorder from which they do not recover. It is found that the time for emergence of this collapse after the introduction of the forcing disturbance has a close correspondence with the theoretical period of one `evolutionary' cycle of momentum exchange between the main motion and the secondary oscillation.
Melissari.MMTB.2005
{Measurement of magnitude and direction of velocity in high-temperature liquid metals. Part I: Mathematical modeling}
Melissari and Argyropoulos
Metall. Trans. B
36B
691--700
(2005)
Melville.ARFM.1996
The Role of Surface-Wave Breaking in Air-Sea Interaction
Melville
Annu. Rev. Fluid Mech.
28
279--321
(1996)
The Role of Surface-Wave Breaking in Air-Sea Interaction.pdf
Breaking serves to limit the height of surface waves, mix the surface waters,
generate ocean currents, and enhance air-sea fluxes of heat, mass, and momen-
tum through the generation of turbulence and the entrainment of air. Breaking
may result from intrinsic instabilities of deep-water waves or through wave-
wave, wave-current, and wind-wave interactions. Observations in the field are
made difficult by the fact that breaking is a strongly nonlinear intermittent pro-
cess occurring over a wide range of scales. Controlled laboratory studies of
breaking have proven useful in measuring the scaling relationships between the
surface wave field and the kinematics and dynamics of breaking. Our inability
to predict the occurrence and dynamics of breaking is a major impediment to
the development of better wind-wave and mixed-layer models. Modern acoustic
and electromagnetic oceanographic instrumentation should lead to significantly
improved measurements of breaking in the near future.
Meneguzzi.PRL.1981
Helical and Nonhelical Turbulent Dynamos
Meneguzzi and Frisch and Pouquet
prl
47
1060--1064
(1981)
10.1103/PhysRevLett.47.1060
Merrill
The Magnetic Field of the Earth
Merrill and McElhinny and McFadden
(1996)
Messer.PP.2005
Observation of momentum confinement time scalings in a rotating plasma
Messer and Ellis and Case and Gupta and Hassam and Lunsford and Teodorescu
pp
12
062509
(2005)
Meyers.PhD.1990
{Laboratory studies of coherent structures in quasi-geostrophic flows}
{Meyers}
(1990)
Laboratory studies of coherent structures in quasi-geostrophic.pdf
http://chaos.ph.utexas.edu/research/meyersbook.pdf
Mikhailovskii.PPCF.2009
Ideal instabilities in a high-{$\beta$} rotating cylindrical plasma in the presence of an azimuthal magnetic field and a gravitational field
Mikhailovskii and Fridman and Churikov and Pustovitov and Smolyakov
Plasma Physics and Controlled Fusion
51
(2009)
Ideal instabilities in a high-$\beta$ rotating cylindrical.pdf
10.1088/0741-3335/51/4/045003
Magnetohydrodynamic (MHD) theory of ideal instabilities in a high-b rotating cylindrical plasma with an azimuthal magnetic field and a radial gravitational field is developed (b is the ratio of the plasma and magnetic field pressures). The basis of this theory is a system of two first-order differential equations for the Frieman-Rotenberg variable (the sum of the perturbed plasma and magnetic field pressures) and the radial plasma displacement, which leads to the second-order differential equation for the displacement. The sausage instability criterion is derived which generalizes the earlier results for a plasma without gravitation. It is shown that this instability can occur for both the decreasing and increasing plasma pressures. The non-axisymmetric modes are also considered. This analysis is related to the MHD instability theory in a nonrotating plasma dealing with snake instabilities. A number of rotational and gravitational effects on both the m = 1 and m > 1 modes are revealed, where m is the azimuthal mode number. The eigenmode equation describing the Suydam modes in the presence of rotational and gravitational effects is derived. These modes can be responsible, in particular, for the Velikhov and rotational-convective instabilities.
Miles.JFM.1957
{On the generation of surface waves by shear flows}
Miles
J. Fluid Mech.
3
185--204
(1957)
On the generation of surface waves by shear flows.pdf
doi:10.1017/S0022112057000567
A mechanism for the generation of surface waves by a parallel shear flow U(y) is developed on the basis of the inviscid Orr-Sommerfeld equation. It is found that the rate at which energy is transferred to a wave of speed c is proportional to the profile curvature -U"(y) at that elevation where U = c. The result is applied to the generation of deep-water gravity waves by wind. An approximate solution to the boundary value problem is developed for a logarithmic profile and the corresponding spectral distribution of the energy transfer coefficient calculated as a function of wave speed. The minimum wind speed for the initiation of gravity waves against laminar dissipation in water having negligible mean motion is found to be roughly 100cm/sec. A spectral mean value of the sheltering coefficient, as defined by Munk, is found to be in order-of-magnitude agreement with total wave drag measurements of Van Dorn. It is concluded that the model yields results in qualitative agreement with observation, but truly quantitative comparisons would require a more accurate solution of the boundary value problem and more precise data on wind profiles than are presently available. The results also may have application to the flutter of membranes and panels.
Mininni.PRE.2005
Low magnetic Prandtl number dynamos with helical forcing
Mininni and Montgomery
pre
72
056320
(2005)
http://link.aps.org/abstract/PRE/v72/e056320
Mininni.PRE.2005b
Shell-to-shell energy transfer in magnetohydrodynamics. II. Kinematic dynamo
Mininni and Alexakis and Pouquet
pre
72
046302
(2005)
http://link.aps.org/abstract/PRE/v72/e046302
Mirnov.JNM.1992
{Liquid-metal tokamak divertors}
Mirnov and Dem'yanenko and Murav'ev
J. Nucl. Mat.
196
45--49
(1992)
Liquid-metal tokamak divertors.pdf
10.1016/S0022-3115(06)80010-3
Both limiters and divertor plates of the reactor scale tokamaks are known to be subjected to extremely high heat loads. The problem of quasistantionary heat fluxes (not, vert, similar107 W/m2), removal, and even the more severe problem of plates protection against impulse heat release on the order of not, vert, similar107 J/m2 during (0.1−1)×10−3 s, are the most critical issues related to divertor regimes in tokamaks. Melting, cracking and other damages of plasma facing components may occur in these regimes. Thus a demand arose to provide the possibility to replace these critical components easily. The easiest possible solution is to replace the traditional contact refractory materials with liquid metals. The simplest realization of the idea was proposed already in the UWMAK project, where a rigid divertor plate was replaced by liquid lithium flow. However, some intrinsic properties of lithium impede its practical application: 1) burning under contact with water; 2) small difference between melting and boiling temperatures. Another candidate material, liquid Ga, is believed to be more adequate (Tm=30$\,^{\circ}$C, Tb=2400$\,^{\circ}$C). On the T-3M tokamak the first encouraging experiments were performed where a liquid Ga jet-drop curtain was tested as a tokamak limiter. The limiter is analogous to one which uses small refractory balls falling down through the plasma column edge. Experiments with a liquid Ga sheet limiter have also started. Experimental results and possible perspectives are discussed.
Moffatt
Magnetic field generation in electrically conducting fluids
Moffatt
(1978)
Magnetic field generation in electrically conducting.pdf
Moffatt.JFM.1961
The amplification of a weak applied magnetic field by turbulence in fluids of moderate conductivity
Moffatt
jfm
11
625--635
(1961)
Mohanty.JFM.1978
Laminar flow in the enterance region of a smooth pipe
Mohanty and Asthana
jfm
90
433-447
(1978)
Molokov.ANL.2000
{Review of free-surface MHD experiments and modeling.}
Molokov and Reed
(2000)
Review of free-surface MHD experiments and modeling..PDF
10.2172/757509
This review paper was prepared to survey the present status of analytical and experimental work in the area of free surface MHD and thus provide a well informed starting point for further work by the Advanced Limiter-diverter Plasma-facing Systems (ALPS) program. ALPS were initiated to evaluate the potential for improved performance and lifetime for plasma-facing systems. The main goal of the program is to demonstrate the advantages of advanced limiter/diverter systems over conventional systems in terms of power density capability, component lifetime, and power conversion efficiency, while providing for safe operation and minimizing impurity concerns for the plasma. Most of the work to date has been applied to free surface liquids. A multi-disciplinary team from several institutions has been organized to address the key issues associated with these systems. The main performance goals for advanced limiters and diverters are a peak heat flux of >50 MW/m{sup 2}, elimination of a lifetime limit for erosion, and the ability to extract useful heat at high power conversion efficiency ({approximately}40%). The evaluation of various options is being conducted through a combination of laboratory experiments, modeling of key processes, and conceptual design studies.
Moon.CPC.1979
Numerical Evaluation of Geomagnetic Dynamo Integrals ({E}lsasser and {A}dams--{G}aunt Integrals)
Moon
cpc
16
267--271
(1979)
Morley.FED.2004
{Progress on the modeling of liquid metal, free surface, MHD flows for fusion liquid walls}
Morley and Smolentsev and Munipalli and Ni and Gao and Abdou
Fusion Eng. \& Design
72
3--34
(2004)
Progress on the modeling of liquid metal, free.pdf
The proposed use of a flowing liquid metal layers as virtual first-walls for magnetic fusion energy reactors has prompted the development of numerical models capable of predicting the motion of such free surface liquid-metal flows within complex geometry boundaries and in the presence of strong magnetic fields. Several model variants were developed that utilize the assumption of toroidal axisymmetry to simplify the governing Navier--Stokes and Maxwell's equations to a 2D form. Typically an induced magnetic field formulation has been used to model eddy current formation and various numerical methods and free surface tracking techniques (including height function and volume-of-fluid) have been employed. These axisymmetric models predict a variety of interesting behavior including the effect of toroidal field gradients on the velocity profiles and stability, and the effect of surface-normal magnetic field components on toroidal motion and flow thickness. However, axisymmetric models cannot be used to simulate the true 3D geometry and magnetic field configuration of a magnetic fusion reactor. And so, a 3D, flexible geometry, multiple material, free surface magnetohydrodynamic (MHD) solver called HIMAG has been developed over the past several years. The HIMAG formulation is described in detail along with the results of several initial benchmark problems. Preliminary data from the application of HIMAG to several fusion relevant liquid wall problems including: (1) motion of lithium in a new sample holder for the Diverter Materials Evaluation System (DiMES) experiment on the DIII-D tokamak facility; (2) motion of gallium alloy in a quasi-2D film flow test section in the MTOR facility; (3) motion of gallium alloy in a 3D field film flow test section in the MTOR facility; are also presented and discussed. Finally, future plans for the HIMAG code, including application to the simulation of the effect of insulator coating cracks on closed channel MHD flows, are described.
Morley.FST.2003
The MTOR LM-MHD flow facility, and preliminary experimental investigation of thin layer, liquid metal flow in a 1/R toroidal magnetic field
Morley and Burris
Fusion Sci. and Tech.
(2003)
The MTOR LM-MHD flow facility, and preliminary.pdf
Morley.RSI.2008
GaInSn usage in the research laboratory
Morley and Burris and Cadwallader and Nornberg
Rev. Sci. Instr.
79
056107--3
(2008)
GaInSn usage in the research laboratory.pdf
http://link.aip.org/link/?RSI/79/056107/1
10.1063/1.2930813
Muller
{The Karlsruhe Dynamo Experiment}
Müller and Stieglitz and Horanyi
(2002)
http://bibliothek.fzk.de/zb/berichte/FZKA6756.pdf
Muller.JFM.2004
A two-scale hydromagnetic dynamo experiment
Müller and Stieglitz and Horany
J. Fluid Mech.
498
31-71
(2004)
http://www.journals.cambridge.org/action/displayAbstract?fromPage=online&aid=195287
Muller_and_Buhler
{Magnetofluiddynamics in Channels and Containers}
Müller and Bühler
(2001)
Magnetofluiddynamics in Channels and Containers.pdf
http://books.google.com/books?id=twDBsjUkulcC
This book serves as an introduction to magnetohydrodynamics (MHD) for graduate and advanced undergraduate engineering students. It may be used by engineers and physicists in research institutions and industry to become familiar with the particular phenomena of magnetothermohydraulics in technical liquid metal flows influenced by magnetic fields. The starting point of the book is the outcome of a recent nuclear fusion project. Therefore, it contains many new results that can be utilized for the design and optimization of various technical systems and processes.
NR
Numerical Recipes in C: The Art of Scientific Computing
Press and Teukolsky and Vetterling and Flannery
(2002)
http://library.lanl.gov/numerical/bookcpdf.html
Nagaosa.PF.1999
Direct numerical simulation of vortex structures and turbulent scalar transfer across a free surface in a fully developed turbulence
Nagaosa
Phys. Fluids
11
1581
(1999)
Direct numerical simulation of vortex structures.pdf
10.1063/1.870020
Dynamics of well-organized tube-like coherent structures under a free surface and turbulent scalar transfer across the free surface in fully developed turbulent flow in an open channel is investigated. A direct numerical simulation of the three-dimensional Navier--Stokes equations is used to obtain the structure of the free-surface turbulence. First, the effect of the free surface on fully developed turbulence statistics is described. Anisotropy of velocity and vorticity under the free surface are given. Next, the dynamics of the intermittent vortex tubes beneath the free surface are stated. The genesis and development of these coherent structures and their interactions with the free surface are demonstrated. The role of the vortex/surface interactions on the dynamics of turbulence under the free surface, particularly intercomponent energy transfer due to the pressure--strain effect, is discussed. In addition, passive scalar transfer across the free surface is studied. Finally, the promotion of turbulent scalar transfer at the free surface by the vortex/interface interactions is discussed.
Nagata.GAFD.1985
Shear flow instability of rotating hydromagnetic fluids
Nagata
Geophysical & Astrophysical Fluid Dynamics
33
173 - 184
(1985)
Shear flow instability of rotating hydromagnetic.pdf
http://www.informaworld.com/10.1080/03091928508245428 %@ 0309-1929 %[ September 16, 2008
The effect of an axial magnetic field on the linear stability of shear flows in rotating systems is examined by extending Busse's analysis of the nonmagnetic case to fluids of high magnetic diffusivity in the presence of a magnetic field. The shear is caused by differential rotation which creates slight deviations from a state of rigid rotation, corresponding to a small Rossby number. It is found that the Rossby number for the onset of instability is larger when a magnetic field is present than when it is absent.
Namikawa.GJRAS.1970
Kinematic Dynamo Problem
Namikawa and Matsushita
gjras
19
395--415
(1970)
Narula.FED.2006
Exploring liquid metal plasma facing component (PFC) concepts--Liquid metal film flow behavior under fusion relevant magnetic fields
Narula and Abdou and Ying and Morley and Ni and Miraghaie and Burris
Fusion Eng. \& Design
81
1543--1548
(2006)
Exploring liquid metal plasma facing.pdf
http://www.sciencedirect.com/science/article/B6V3C-4J32JJG-7/1/24470fc6e79cf204500b6a849bee96c0
The use of fast moving liquid metal streams or "liquid walls" as a plasma contact surface is a very attractive option and has been looked upon with considerable interest over the past several years, both by the plasma physics and fusion engineering programs. Flowing liquid walls provide an ever replenishing contact surface to the plasma, leading to very effective particle pumping and surface heat flux removal. A key feasibility issue for flowing liquid metal plasma facing component (PFC) systems, pertains to their magnetohydrodynamic (MHD) behavior under the spatially varying magnetic field environment, typical of a fusion device. MHD forces hinder the development of a smooth and controllable liquid metal flow needed for PFC applications. The present study builds up on the ongoing research effort at UCLA, directed towards providing qualitative and quantitative data on liquid metal free surface flow behavior under fusion relevant magnetic fields.
Nataf.GAFD.2006
Experimental study of super-rotation in a magnetostrophic spherical {C}ouette flow
Nataf and Alboussi\`ere and Brito and Cardin and Gagni\`ere and Jault and Masson and Schmitt
gafd
100
281-298
(2006)
Experimental study of super-rotation in a magnetostrophic spherical.pdf
10.1080/03091920600718426
Ness.Science.1986
Magnetic Fields at {U}ranus
Ness and Acu{\~{n}}a and Behannon and Burlaga and Connerney and Lepping and Neubauer
science
233
85--89
(1986)
Ness.Science.1989
Magnetic Fields at {N}eptune
Ness and Acu{\~{n}}a and Burlaga and Connerney and Lepping and Neubauer
science
246
1473--1478
(1989)
Nezu.JHE.1986
Open-channel flow measurements with a laser doppler anemometer
Nezu and Rodi
J. Hydraul. Eng.
112
335--355
(1986)
Open-channel flow measurements with a laser.pdf
Nezu.JHE.2005
{Open-Channel Flow Turbulence and Its Research Prospect in the 21st Century}
Nezu
J. Hydraul. Eng.
131
229--246
(2005)
Open-Channel Flow Turbulence and Its Research Prospect.pdf
Nobach.EF.1998
{Efficient estimation of power spectral density from laser Doppler anemometer data}
{Nobach} and {Müller} and {Tropea}
Experiments in Fluids
24
499--509
(1998)
Noguchi.2004
Magnetorotational Instability in a {C}ouette Flow of Plasma
Noguchi and Pariev
692
285--292
(2003)
Noguchi.APJ.2002
Magnetorotational Instability in Liquid Metal Couette Flow
{Noguchi} and {Pariev} and {Colgate} and {Beckley} and {Nordhaus}
apj
575
1151-1162
(2002)
Magnetorotational Instability in Liquid Metal Couette.pdf
10.1086/341502
Despite the importance of the magnetorotational instability (MRI) as a fundamental mechanism for angular momentum transport in magnetized accretion disks, it has yet to be demonstrated in the laboratory. A liquid sodium dynamo experiment at the New Mexico Institute of Mining and Technology provides an ideal environment to study the MRI in a rotating metal annulus (Couette flow). A local stability analysis is performed as a function of shear, magnetic field strength, magnetic Reynolds number, and turbulent Prandtl number. The latter takes into account the minimum turbulence induced by the formation of an Ekman layer against the rigidly rotating end walls of a cylindrical vessel. Stability conditions are presented, and unstable conditions for the sodium experiment are compared with another proposed MRI experiment with liquid gallium. Because of the relatively large magnetic Reynolds number achievable in the sodium experiment, it should be possible to observe the excitation of the MRI for a wide range of wavenumbers and to further observe the transition to the turbulent state.
Noir.GRL.2001
Experimental evidence of inertial waves in a precessing spheroidal cavity
Noir and Brito and Aldridge and Cardin
Geophys. Res. Lett
28
3785--3788
(2001)
Experimental evidence of inertial waves in a precessing.pdf
Nordlund.APJ.1992
Dynamo action in stratified convection with overshoot
Nordlund and Brandenburg and Jennings and Rieutord and Roukolainen and Stein and Tuominen
apj
392
647
(1992)
Nornberg.PP.2006
Measurements of the Magnetic Field Induced by a Turbulent Flow of Liquid Metal
Nornberg and Spence and Kendrick and Jacobson and Forest
pp
13
055901
(2006)
Measurements of the Magnetic Field Induced by a Turbulent.pdf
10.1063/1.2173614
Nornberg.PRL.2006
Intermittent Magnetic Field Excitation by a Turbulent Flow of Liquid Sodium
Nornberg and Spence and Kendrick and Jacobson and Forest
Physical Review Letters
97
044503--4
(2006)
Intermittent Magnetic Field Excitation by a Turbulent.pdf
http://link.aps.org/abstract/PRL/v97/e044503
10.1103/PhysRevLett.97.044503
The magnetic field measured in the Madison dynamo experiment shows intermittent periods of growth when an axial magnetic field is applied. The geometry of the intermittent field is consistent with the fastest-growing magnetic eigenmode predicted by kinematic dynamo theory using a laminar model of the mean flow. Though the eigenmodes of the mean flow are decaying, it is postulated that turbulent fluctuations of the velocity field change the flow geometry such that the eigenmode growth rate is temporarily positive. Therefore, it is expected that a characteristic of the onset of a turbulent dynamo is magnetic intermittency.
Nornberg.RSI.2008
A liquid metal flume for free surface magnetohydrodynamic experiments
Nornberg and Ji and Peterson and Rhoads
Review of Scientific Instruments
79
094501--7
(2008)
A liquid metal flume for free surface.pdf
http://link.aip.org/link/?RSI/79/094501/1
We present an experiment designed to study magnetohydrodynamic effects in free surface channel flow. The wide aspect ratio channel (the width to height ratio is about 15) is completely enclosed in an inert atmosphere to prevent oxidization of the liquid metal. A custom-designed pump reduces entrainment of oxygen, which was found to be a problem with standard centrifugal and gear pumps. Laser Doppler velocimetry experiments characterize velocity profiles of the flow. Various flow constraints mitigate secondary circulation and end effects on the flow. Measurements of the wave propagation characteristics in the liquid metal demonstrate the surfactant effect of surface oxides and the damping of fluctuations by a cross-channel magnetic field.
Nornberg.Thesis.2006
{The role of MHD turbulence in magnetic self-excitation: a study of the Madison Dynamo Experiment}
Nornberg
(2006)
The role of MHD turbulence in magnetic self-excitation: a study.pdf
Nygren.FED.2002
{Actively cooled plasma facing components for long pulse high power operation}
Nygren
Fusion Eng. \& Design
60
547--564
(2002)
Nyquist.TAIEE.1928
Certain topics in telegraph transmission theory
Nyquist
taiee
47
617--644
(1928)
Odier.PRE.1998
Advection of a magnetic field by a turbulent swirling flow
Odier and Pinton and Fauve
pre
58
7397--7401
(1998)
10.1103/PhysRevE.58.7397
Ogilvie.MNRAS.1996
{The non-axisymmetric instability of a cylindrical shear flow containing an azimuthal magnetic field}
{Ogilvie} and {Pringle}
Mon. Not. R. Astron. Soc.
279
152-164
(1996)
The non-axisymmetric instability of a cylindrical shear flow.pdf
http://adsabs.harvard.edu/abs/1996MNRAS.279..152O
The stability of a differentially rotating, cylindrical fluid body containing an azimuthal magnetic field is investigated by solving the linear eigenvalue problem for non-axisymmetric perturbations. The model system consists of a perfectly conducting, ideal, incompressible fluid contained within cylindrical boundaries. It is found that exponentially growing modes are always present when the angular velocity decreases outwards, unless the magnetic field exceeds a certain strength. In the weak-field limit, growth rates approaching the Oort constant A can be attained. In the absence of diffusion, the instability grows preferentially at arbitrarily small scales. A purely magnetic instability can also be present, and persists when the magnetic field is arbitrarily strong. The growing modes are found to depend on the presence of at least one radial boundary. The structure of the spectrum of discrete eigenvalues is discussed in relation to the Alfven continua, and the limit points of eigenvalues at large axial wavenumber are obtained. Analogous behaviour is found in a system with Cartesian geometry, which more accurately describes models currently being used to study non-linear behaviour in accretion discs.
Olson.GJI.2002
The time-averaged magnetic field in numerical dynamos with non-uniform boundary heat flow
Olson and Christensen
gji
151
809--823
(2002)
Olson.Nature.1997
Geophysics: Probing {E}arth's dynamo
Olson
nature
389
337--338
(1997)
10.1038/38622
Orszag.JFM.1970
Analytical theories of turbulence
Orszag
jfm
41
363--386
(1970)
Analytical theories of turbulence.pdf
10.1017/S0022112070000642
This paper surveys the current state of analytical attempts at a theory of turbulence. The formulation of the problem in terms of moments is discussed. The difficulty posed by the closure problem is examined in detail using the quasinormal approximation as an example. The notion of dynamical relaxation by non-linear scrambling leads to the introduction of eddy relaxation times and the direct-interaction approximation. The properties of the direct-interaction approximation are indicated. Finally, a comparison is made between numerical solution of the equations of turbulence their and direct numerical simulation of the Navier--Stokes equations.
Ossendrijver.AAR.2003
The solar dynamo
Ossendrijver
aar
11
287--367
(2003)
Ozaki.ETFS.2002
High time resolution ultrasonic velocity profiler
Ozaki and Kawaguchi and Takeda and Hishida and Maeda
Experimental Thermal and Fluid Science
26
253--258
(2002)
http://www.sciencedirect.com/science/article/B6V34-45D18NF-C/2/6bb4e90b6a6ecfb5c4eb5d08cc576b44
Panton.AMR.2005
{Review of Wall Turbulence as Described by Composite Expansions}
Panton
App. Mech. Rev.
58
1
(2005)
Papaloizou.MNRAS.1984
The dynamical stability of differentially rotating discs with constant specific angular momentum
Papaloizou and Pringle
Mon. Not. R. Astron. Soc.
208
721--750
(1984)
The dynamical stability of differentially rotating discs.pdf
http://adsabs.harvard.edu/abs/1984MNRAS.208..721P
The dynamical stability of a differentially rotating disc (or torus) of fluid of uniform entropy and uniform specific angular momentum is investigated. Such a fluid is neutrally stable to axisymmetric perturbations. Non-axisymmetric perturbations are considered as part of a global stability analysis. A general study of the normal mode eigenvalue problem and the explicit analytic solution of a pair of particular limiting cases are presented. The fastest growing eigenmodes by numerical integration of the full linearized equations for more general cases are derived. The overall result is that the tori are unstable to low order non-axisymmetric modes and that the modes grow on a dynamical time-scale. Because of the strength of the instability, similar unstable modes must exist in tori of non-uniform entropy or of non-uniform specific angular momentum.
Papaloizou:1995aa
Theory of Accretion Disks I: Angular Momentum Transport Processes
Papaloizou and Lin
Annual Review of Astronomy and Astrophysics
33
505-540
(1995)
Theory of Accretion Disks I: Angular Momentum.pdf
http://arjournals.annualreviews.org/doi/abs/10.1146/annurev.aa.33.090195.002445
Accretion disk flow is a common phenomenon in astrophysics. It provides
the nursery for planetary system formation and the channel for mass transfer in
interacting binary stars. Such flows are also associated with the central engine
for active galactic nuclei.
Mass is redistributed in accretion disks as a consequence of angular momentum
transfer. The identification of the dominant process involved is an important task
in the development of accretion disk theory. Here, we review recent theoretical
investigations on several important physical processes, including: 1. the removal
of angular momentum from disks through hydromagnetic winds, 2. the amplifica-
tion of local viscous stress through the onset of turbulence resulting from possible
hydromagnetic, convective, or shear flow instabilities, 3. the transport of angular
momentum carried by propagating waves, and 4. torque resulting from the pres-
ence of nonaxisymmetric unstable modes in self-gravitating and geometrically
thick disks. Because of the technical nature of this subject, we present some of
the mathematical formalisms in a pedagogical manner. We focus our attention
on the physical discussion of the necessary conditions for each process to operate
and the efficiency of angular momentum transfer to be expected. In Part II of
this review, we shall present observational evidences and discuss applications of
theoretical results in different astrophysical context.
Parker.AJ.1955b
{Hydromagnetic Dynamo Models.}
{Parker}
apj
122
293--314
(1955)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1955ApJ...122..293P&db_key=AST
Parker.AJ.1971d
{The Generation of Magnetic Fields in Astrophysical Bodies.IV. The Solar and Terrestrial Dynamos}
{Parker}
apj
164
491
(1971)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1971ApJ...164..491P&db_key=AST
Parker.APJ.1955a
{The Formation of Sunspots from the Solar Toroidal Field.}
{Parker}
apj
121
491
(1955)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1955ApJ...121..491P&db_key=AST
Parker.APJ.1970a
{The Origin of Magnetic Fields}
{Parker}
apj
160
383
(1970)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1970ApJ...160..383P&db_key=AST
10.1086/150442
Parker.APJ.1970b
{The Generation of Magnetic Fields in Astrophysical Bodies. I. The Dynamo Equations}
{Parker}
apj
162
665
(1970)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1970ApJ...162..665P&db_key=AST
Parker.APJ.1971a
{The Generation of Magnetic Fields in Astrophysical Bodies. II. The Galactic Field}
{Parker}
apj
163
255
(1971)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1971ApJ...163..255P&db_key=AST
Parker.APJ.1971b
{The Generation of Magnetic Fields in Astrophysical Bodies. III. Turbulent Diffusion of Fields and Efficient Dynamos}
{Parker}
apj
163
279
(1971)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1971ApJ...163..279P&db_key=AST
Parker.APJ.1971c
{The Generation of Magnetic Fields in Astrophysical Bodies.IV. The Solar and Terrestrial Dynamos}
{Parker}
apj
164
491
(1971)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1971ApJ...164..491P&db_key=AST
Parker.APJ.1971d
{The Generation of Magnetic Fields in Astrophysical Bodies. V. Behavior at Large Dynamo Numbers}
{Parker}
apj
165
139
(1971)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1971ApJ...165..139P&db_key=AST
Parker.APJ.1971e
{The Generation of Magnetic Fields in Astrophysical Bodies.VI. Periodic Modes of the Galactic Field}
{Parker}
apj
166
295
(1971)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1971ApJ...166..295P&db_key=AST
Parker.APJ.1971f
{The Generation of Magnetic Fields in Astrophysical Bodies. VII. The Internal Small-Scale Fields}
{Lerche} and {Parker}
apj
168
231
(1971)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1971ApJ...168..231L&db_key=AST
Parker.APJ.1971g
{The Generation of Magnetic Fields in Astrophysical Bodies. VII. Dynamical Considerations}
{Parker}
apj
168
239
(1971)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1971ApJ...168..239P&db_key=AST
Parker.APJ.1972h
{The Generation of Magnetic Fields in Astrophysical Bodies.IX. a Solar Dynamo Based on Horizontal Shear}
{Lerche} and {Parker}
apj
176
213
(1972)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1972ApJ...176..213L&db_key=AST
Parker.APJ.1975a
{The generation of magnetic fields in astrophysical bodies. X - Magnetic buoyancy and the solar dynamo}
{Parker}
apj
198
205-209
(1975)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1975ApJ...198..205P&db_key=AST
Parker.APJ.1975b
{The escape of magnetic flux from a turbulent body of gas}
{Parker}
apj
202
523-527
(1975)
Parker.APJ.1977
{The generation of magnetic fields in astrophysical bodies. XI - The effect of magnetic buoyancy on the growth and migration of dynamo waves in the sun}
{Parker}
apj
215
370-373
(1977)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1977ApJ...215..370P&db_key=AST
Peffley.PRE.2000
Toward a self-generating dynamo: The role of turbulence
Peffley and Cawthorne and Lathrop
pre
61
5287--5294
(2000)
Toward a self-generating dynamo: The role of turbulence.pdf
10.1103/PhysRevE.61.5287
Pekeris.PTRSLA.1973
Kinematic Dynamos and the {E}arth's Magnetic Field
Pekeris and Accad and Shkoller
ptrsla
275
425--461
(1973)
Pessah.AJ.2005
The Stability of Magnetized Rotating Plasmas with Superthermal Fields
Pessah and Psaltis
Astrophys. J.
628
879-901
(2005)
The Stability of Magnetized Rotating Plasmas with.pdf
http://www.journals.uchicago.edu/doi/abs/10.1086/430940
During the last decade it has become evident that the magnetorotational instability is at the heart of the enhanced angular momentum transport in weakly magnetized accretion disks around neutron stars and black holes. In this paper we investigate the local linear stability of differentially rotating, magnetized flows and the evolution of the magnetorotational instability beyond the weak-field limit. We show that, when superthermal toroidal fields are considered, the effects of both compressibility and magnetic tension forces, which are related to the curvature of toroidal field lines, should be taken fully into account. We demonstrate that the presence of a strong toroidal component in the magnetic field plays a nontrivial role. When strong fields are considered, the strength of the toroidal magnetic field not only modifies the growth rates of the unstable modes but also determines which modes are subject to instabilities. We find that, for rotating configurations with Keplerian laws, the magnetorotational instability is stabilized at low wavenumbers for toroidal Alfvén speeds exceeding the geometric mean of the sound speed and the rotational speed. For a broad range of magnetic field strengths, we also find that two additional distinct instabilities are present; they both appear as the result of coupling between the modes that become the Alfvén and the slow modes in the limit of no rotation. We discuss the significance of our findings for the stability of cold, magnetically dominated, rotating fluids and argue that, for these systems, the curvature of toroidal field lines cannot be neglected even when short-wavelength perturbations are considered. We also comment on the implications of our results for the validity of shearing box simulations in which superthermal toroidal fields are generated.
Pessah.AJ.2008
Viscous, Resistive Magnetorotational Modes
Pessah and Chan
Astro. Phys. J.
684
498--514
(2008)
Viscous, Resistive Magnetorotational Modes.pdf
10.1086/589915
We carry out a comprehensive analysis of the behavior of the magnetorotational instability (MRI) in viscous, resistive plasmas. We find exact, nonlinear solutions of the nonideal magnetohydrodynamic (MHD) equations describing the local dynamics of an incompressible, differentially rotating background threaded by a vertical magnetic field when disturbances with wavenumbers perpendicular to the shear are considered. We provide a geometrical description of these viscous, resistive MRI modes and show how their physical structure is modified as a function of the Reynolds and magnetic Reynolds numbers. We demonstrate that when finite dissipative effects are considered, velocity and magnetic field disturbances are no longer orthogonal (as is the case in the ideal MHD limit) unless the magnetic Prandtl number is unity. We generalize previous results found in the ideal limit and show that a series of key properties of the mean Reynolds and Maxwell stresses also hold for the viscous, resistive MRI. In particular, we show that the Reynolds stress is always positive and the Maxwell stress is always negative. Therefore, even in the presence of viscosity and resistivity, the total mean angular momentum transport is always directed outward. We also find that, for any combination of the Reynolds and magnetic Reynolds numbers, magnetic disturbances dominate both the energetics and the transport of angular momentum and that the total mean energy density is an upper bound for the total mean stress responsible for angular momentum transport. The ratios between the Maxwell and Reynolds stresses and between magnetic and kinetic energy densities increase with decreasing Reynolds numbers for any magnetic Reynolds number; the lowest limit of both ratios is reached in the ideal MHD regime. The analytical results presented here provide new benchmarks for the various algorithms employed to solve the viscous, resistive MHD equations in the shearing box approximation.
Pessah.AJL.2007
Angular Momentum Transport in Accretion Disks: Scaling Laws in MRI-driven Turbulence
Pessah and Chan and Psaltis
Astrophys. J.
668
L51-L54
(2007)
Angular Momentum Transport in Accretion Disks:.pdf
http://www.journals.uchicago.edu/doi/abs/10.1086/522585
We present a scaling law that predicts the values of the stresses obtained in numerical simulations of saturated MRI-driven turbulence in nonstratified shearing boxes. It relates the turbulent stresses to the strength of the vertical magnetic field, the sound speed, the vertical size of the box, and the numerical resolution and predicts accurately the results of 35 numerical simulations performed for a wide variety of physical conditions. We use our result to show that the saturated stresses in simulations with zero net magnetic flux depend linearly on the numerical resolution and would become negligible if the resolution were set equal to the natural dissipation scale in astrophysical disks. We conclude that in order for MRI-driven turbulent angular momentum transport to be able to account for the large value of the effective alpha viscosity inferred observationally, the disk must be threaded by a significant vertical magnetic field and the turbulent magnetic energy must be in near equipartition with the thermal energy. This result has important implications for the spectra of accretion disks and their stability.
Pessah.MNRAS.2006
The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs
Martin E. Pessah, Chi-kwan Chan
Mon. Not. R. Astron. Soc.
372
183-190
(2006)
The signature of the magnetorotational instability in the Reynolds and Maxwell.pdf
http://dx.doi.org/10.1111/j.1365-2966.2006.10824.x
10.1111/j.1365-2966.2006.10824.x
Petitdemange.GRL.2008
{Magnetostrophic MRI in the Earth's outer core}
Petitdemange and Dormy and Balbus
Geophys. Res. Lett
35
L15305
(2008)
Magnetostrophic MRI in the Earth's outer core0.pdf
10.1029/2008GL034395
We show that a simple, modified version of the
Magnetorotational Instability (MRI) can develop in the
outer liquid core of the Earth, in the presence of a background
shear. It requires either thermal wind, or a primary instability,
such as convection, to drive a weak differential rotation
within the core. The force balance in the Earth's core is very
unlike classical astrophysical applications of the MRI (such
as gaseous disks around stars). Here, the weak differential
rotation in the Earth core yields an instability by its
constructive interaction with the planet's much larger
rotation rate. The resulting destabilising mechanism is
just strong enough to counteract stabilizing resistive
effects, and produce growth on geophysically interesting
timescales. We give a simple physical explanation of the
instability, and show that it relies on a force balance
appropriate to the Earth's core, known as magnetostrophic
balance.geodynamo [see, e.g., Acheson, 1983; Ogden and Fearn,
1995; Fearn et al., 1997]. But in previous calculations
the emphasis has been upon purely azimuthal fields,
nonaxisymmetric disturbances, and magnetic instabilities.
In this work, the dynamical focus is much different. Here
the magnetic coupling is to the poloidal field components,
axisymmetric disturbances are front and center, and the
instability, while relying on the presence of a magnetic
field, has its seat of free energy entirely in differential
rotation. The MRI is a somewhat novel concept in this
context, and is worthy of study in isolation. Fortunately,
it can be understood in very direct and simple physical
terms.
[4] The Earth's core is, by comparison to accretion disks,
a relatively small object, in which resistive effects are on an
equal footing with dynamical processes. The rotation prop-
Petrelis.PP.2003
Bounds on dissipation in magnetohydrodynamic problems in plane shear geometry
Pétrélis and Alexakis and Doering and Morrison
Phys. Plasmas
10
4314
(2003)
Petrelis.PRL.2003
Nonlinear Magnetic Induction by Helical Motion in a Liquid Sodium Turbulent Flow
P\'{e}tr\'{e}lis and Bourgoin and Mari\'{e} and Burguete and Chiffaudel and Daviaud and Fauve and Odier and Pinton
prl
90
174501--174505
(2003)
http://link.aps.org/abstract/PRL/v90/e174501
Pinton.JPII.1994
{Correction to the Taylor hypothesis in swirling flows}
Pinton and Labbé
J. Phys. II France
4
1461--1468
(1994)
10.1051/jp2:1994211
Piro.APJ.2007
Turbulent Mixing in the Surface Layers of Accreting Neutron Stars
Piro and Bildsten
Astrophys. J.
663
1252--1268
(2007)
Turbulent Mixing in the Surface Layers of Accreting.pdf
10.1086/518687
Ponomarenko.JAMTP.1970
Theory of the hydromagnetic generator
Ponomarenko
jamtp
14
775--778
(1973)
Theory of the hydromagnetic generator.pdf
10.1007/BF00853190
Ponty.PRL.2005
{Numerical Study of Dynamo Action at Low Magnetic Prandtl Numbers}
Ponty and Mininni and Montgomery and Pinton and Politano and Pouquet
prl
94
164502
(2005)
http://link.aps.org/abstract/PRL/v94/e164502
Portelli.PRL.2003
Intermittency and Non-Gaussian Fluctuations of the Global Energy Transfer in Fully Developed Turbulence
Portelli and Holdsworth and Pinton
prl
90
104501
(2003)
http://link.aps.org/abstract/PRL/v90/e104501
Potherat.JFM.2000
An effective two-dimensional model for MHD flows with transverse magnetic field
POTHÉRAT and SOMMERIA and MOREAU
Journal of Fluid Mechanics
424
75--100
(2000)
An effective two-dimensional model for MHD flows with.pdf
This paper presents a model for quasi-two-dimensional MHD flows between two planes with small magnetic Reynolds number and constant transverse magnetic field orthogonal to the planes. A method is presented that allows three-dimensional effects to be taken into account in a two-dimensional equation of motion thanks to a model for the transverse velocity profile. This model is obtained by using a double perturbation asymptotic development both in the core flow and in the Hartmann layers arising along the planes. A new model is thus constructed that describes inertial effects in these two regions. Two separate classes of phenomena are found: one related to inertial effects in the Hartmann layer gives a model for recirculating flows and the other introduces the possibility of having a transverse dependence of the velocity profile in the core flow. The `recirculating' velocity profile is then introduced in the transversally averaged equation of motion in order to provide an effective two-dimensional equation of motion. Analytical solutions of this model are obtained for two experimental configurations: isolated vortices generated by a point electrode and axisymmetric parallel layers occurring in the MATUR (MAgneticTURbulence) experiment. The theory is found to give a satisfactory agreement with the experiment so that it can be concluded that recirculating flows are actually responsible for both vortex core spreading and excessive dissipative behaviour of the axisymmetric sidewall layers
Pouquet.JFM.1978a
{Strong MHD helical turbulence and the nonlinear dynamo effect}
Pouquet and Frisch and L\'erot
jfm
77
321--354
(1976)
Pouquet.JFM.1978b
Numerical simulations of helical magnetohydrodynamic turbulence
Pouquet and Patterson
jfm
85
305--323
(1978)
Proctor.GAFD.1977
{On Backus' Necessary Condition for Dynamo Action in a Conducting Sphere}
{Proctor}
Geophys. Astrophys. Fluid Dynamics
9
89--93
(1977)
Pushkarev.PRL.1996
Turbulence of Capillary Waves
Pushkarev and Zakharov
Phys. Rev Lett.
76
(1996)
Turbulence of Capillary Waves.pdf
http://link.aps.org/abstract/PRL/v76/p3320
Radler.PRE.2003
Contributions to the theory of a two-scale homogenous dynamo experiment
R\"{a}dler and Brandenburg
pre
67
26401--26411
(2003)
Rappaport.PP.2001
Coupling of the resistive wall mode to liquid wall surface modes
Rappaport
pp
8
3620-3629
(2001)
http://link.aip.org/link/?PHP/8/3620/1
Rashidi.PF.1997
Burst--interface interactions in free surface turbulent flows
Rashidi
Physics of Fluids
9
3485--3501
(1997)
Burst--interface interactions in free surface turbulent.pdf
http://link.aip.org/link/?PHF/9/3485/1
Interactions of bursting events (i.e., ejections and inflows) with the free surface in turbulent channel flows have been studied using oxygen bubble visualization and image processing techniques. Experiments indicate that the flow is dominated by the generation of wall ejections, formation of spanwise "upsurging vortices", and interaction of such structures with the free surface. The spanwise upsurging vortices are seen to evolve near the wall, reach the free surface, form surface patches, roll back in form of spanwise "downswinging vortices", and mix into the bulk flow. Furthermore, there are evidence of horseshoe and hockeystick type vortices in relation to the bursting events. Measurements of surface characteristics show that the ejection--inflow events are associated with deformation of the free surface and a redistribution of near surface vorticity and velocity fields. It is seen that as upsurging vortices reach the free surface, the surface goes through an elevation or a rise, whereas the surface falls when downswinging vortices of the inflowing fluid return toward the wall. These effects are enhanced as the flow Reynolds number is increased. Conditional averaging of the velocity fields shows that while the surface rise is associated with an increase in the streamwise component of turbulence intensities throughout the liquid layer, surface falls are associated with a slight decrease in streamwise intensities near the free surface. Near the wall, all components of intensities are higher for the cases with surface rise than they are for the ones with surface fall. Contour color plots of the velocities and intensities near the interface region depicts these results and show an increase in the number of spanwise vortices rolling in the direction of flow during the ejection--inflow events. Based on these results and observation of video sequences, a conceptual illustration of burst--interface interactions has been provided.
Rau.GJI.2000
Core flow inversion tested with numerical dynamo models
Rau and Christensen and Jackson and Wicht
gji
141
485--497
(2000)
Ravelet.PF.2005
{Toward an experimental von K\'arm\'an dynamo: Numerical studies for an optimized design}
Ravelet and Chiffaudel and Daviaud and L\'eorat
pf
17
117104
(2005)
http://link.aip.org/link/?PHF/17/117104/1
Rayleigh.PRSLA.1917
On the Dynamics of Revolving Fluids
Rayleigh
Proc. R. Soc. Lond. A
93
148--154
(1917)
On the Dynamics of Revolving Fluids.pdf
http://dx.doi.org/10.1098/rspa.1917.0010
Redd.PP.2002
{Current drive experiments in the helicity injected torus (HIT--II)}
Redd and Nelson and Jarboe and Gu and Raman and Smith and McCollam
pp
9
2006--2013
(2002)
Reed.JFM.1978
The effect of a transverse magnetic field on shear turbulence
Reed and Lykoudis
J. Fluid Mech.
89
(1978)
The effect of a transverse magnetic field on shear.pdf
Turbulence measurements under the influence of a transverse magnetic field have
been made at Purdue University's Magneto-Fluid-Mechanic Laboratory in a high
aspect ratio channel. The Reynolds number range covered was 35000 < Re 6 282000;
the geometry and experimental conditions were such that the experiment approxi-
mated turbulent Hartmann flow. The aspect ratio of the channel was 6.8 : 1, its walls
were electrically insulated and the working fluid was mercury. Measurements in the
presence of a magnetic field were made of the skin friction coefficient, the mean velocity
profiles, the turbulence intensity profiles (both u' and v`) and the Reynolds stress
profiles.
A sudden change in the damping of the Reynolds stresses was manifested by a
`hump' in the curves of C, versus M/Re taken with the Reynolds number held
constant. This `hump' occurs as a gentle rise and sudden drop to the Hartmann
laminar line of the C, data. Close examination of the fm data near the wall confirms
this behaviour, indicating that the turbulent contribution to the shear stress is the con-
trolling factor in this behaviour of C,. The Reynolds stresses were complete1;y suppressed
to zero at high values of the magnetic field, though the turbulence intensities of u` and
v` were not. The Reynolds stress data are fundamental in revealing the mechanisms
which are at work during the suppression of turbulence by a magnetic field.
It was also found that at high magnetic fields, when most of the turbulence was
damped, the skin friction coefficient fell below the values predicted by Hartmann's
(1937) laminar solution for high values of >!/Re. This result was linked to the presence
of `M-shaped' velocity profiles in the direction perpendicular to both the magnetic
field and the mean velocity vector. The presence of `M-shaped' profiles has not
previously been linked to a reduction in C,.
Reighard.PRL.2001
Turbulent Conductivity Measurements in a Spherical Liquid Sodium Flow
Reighard and Brown
prl
86
2794--2797
(2001)
10.1103/PhysRevLett.86.2794
Rhines.JFM.1975
Waves and turbulence on a beta-plane
Rhines
J. Fluid Mech.
69
417--443
(1975)
Waves and turbulence on a beta-plane.pdf
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=373502&fulltextType=RA&fileId=S0022112075001504
10.1017/S0022112075001504
Two-dimensional eddies in a homogeneous fluid at large Reynolds number, if closely packed, are known to evolve towards larger scales. In the presence of a restoring force, the geophysical beta-effect, this cascade produces a field of waves without loss of energy, and the turbulent migration of the dominant scale nearly ceases at a wavenumber k{$\beta$} = ({$\beta$}\/2U)/12; independent of the initial conditions other than U, the r.m.s. particle speed, and {$\beta$}, the northward gradient of the Coriolis frequency.The conversion of turbulence into waves yields, in addition, more narrowly peaked wavenumber spectra and less fine-structure in the spatial maps, while smoothly distributing the energy about physical space.The theory is discussed, using known integral constraints and similarity solutions, model equations, weak-interaction wave theory (which provides the terminus for the cascade) and other linearized instability theory. Computer experiments with both finite-difference and spectral codes are reported. The central quantity is the cascade rate, defined as{$\backslash$}{$[$}T = 2{$\backslash$}int{\_}0\^{}{\{}{$\backslash$}infty{\}} kF(k)dk/U\^{}3{$\backslash$}langle k{$\backslash$}rangle ,{$\backslash$}{$]$}where F is the nonlinear transfer spectrum and \⟨k\⟩ the mean wavenumber of the energy spectrum. (In unforced inviscid flow T is simply U\−1d\⟨k\⟩\−1\/dt, or the rate at which the dominant scale expands in time t.) T is shown to have a mean value of 3{$\cdot$}0 {$\times$} 10\−2 for pure two-dimensional turbulence, but this decreases by a factor of five at the transition to wave motion. We infer from weak-interaction theory even smaller values for k \≪ k{$\beta$}.After passing through a state of propagating waves, the homogeneous cascade tends towards a flow of alternating zonal jets which, we suggest, are almost perfectly steady. When the energy is intermittent in space, however, model equations show that the cascade is halted simply by the spreading of energy about space, and then the end state of a zonal flow is probably not achieved.The geophysical application is that the cascade of pure turbulence to large scales is defeated by wave propagation, helping to explain why the energy-containing eddies in the ocean and atmosphere, though significantly nonlinear, fail to reach the size of their respective domains, and are much smaller. For typical ocean flows, {\$}k{\_}{\{}{$\backslash$}beta{\}}\^{}{\{}-1{\}} = 70{$\backslash$},{\{}{$\backslash$}rm km{\}} {\$}, while for the atmosphere, {\$}k{\_}{\{}{$\backslash$}beta{\}}\^{}{\{}-1{\}} = 1000{$\backslash$},{\{}{$\backslash$}rm km{\}}{\$}. In addition the cascade generates, by itself, zonal flow (or more generally, flow along geostrophic contours).
Richard.AA.1999
{Turbulence in differentially rotating flows. What can be learned from the Couette-Taylor experiment}
{Richard} and {Zahn}
Astron. Astrophys.
347
734-738
(1999)
Turbulence in differentially rotating flows. What.pdf
The turbulent transport of angular momentum plays an important role in many astrophysical objects, but its modelization is still far from satisfactory. We discuss here what can be learned from laboratory experiments. We analyze the results obtained by Wendt (1933) and Taylor (1936) on the classical Couette-Taylor flow, in the case where angular momentum increases with distance from the rotation axis, which is the most interesting for astrophysical applications. We show that when the gap between the coaxial cylinders is wide enough, the criterion for the onset of the finite amplitude instability can be expressed in terms of a gradient Reynolds number. Based on Wendt's results, we argue that turbulence may be sustained by differential rotation when the angular velocity decreases outward, as in keplerian flows. From the rotation profiles and the torque measurements we deduce a prescription for the turbulent viscosity which is independent of gap width; with some caution it may be applied to stellar interiors and to accretion disks.
Ricou.JHMT.1982
Local velocity and mass transfer measurements in molten metals using an incorporated magnet probe
Ricou and Vives
Int. J. Heat Mass Transfer
25
1579--1588
(1982)
http://dx.doi.org/10.1016/0017-9310(82)90036-9
Roberts.AA.1972
{$\alpha$-Effect Dynamos, by the Bullard-Gellman Formalism}
{Roberts} and {Stix}
Astron. Astrophys.
18
453--466
(1972)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query bibcode=1972A%26A....18..453R&db_key=AST
Roberts.APJ.1987
Time Series Analysis with Clean- Part One- Derivation of a Spectrum
Roberts and Lehar and Dreher
Astrophys. J.
93
968
(1987)
Time Series Analysis with Clean-.pdf
Roberts.ARFM.1972
Magnetohydrodynamics of the Earth's Core
Roberts and Soward
Annu. Rev. Fluid Mech.
4
117--154
(1972)
Magnetohydrodynamics of the Earth's Core.pdf
http://dx.doi.org/10.1146/annurev.fl.04.010172.001001
Roberts.JFM.1979
{On the diffusive instability of some simple steady magnetohydrodynamic flows}
{Roberts} and {Loper}
J. Fluid Mech.
90
641-668
(1979)
On the diffusive instability of some simple steady0.pdf
http://adsabs.harvard.edu/abs/1979JFM....90..641R
10.1017/S0022112079002469
Roberts.JGG.1965
On the analysis of the secular variation, 1, A hydrodynamic contraint: Theory
Roberts and Scott
jgg
17
137--151
(1965)
Roberts.PFB.1993
Homogeneous dynamos: Theory and practice
Roberts and Jensen
pfb
5
2657-2662
(1993)
http://link.aip.org/link/?PHB/5/2657/1
Roberts.PTRSLA.1970
Spatially Periodic Dynamos
Roberts
ptrsla
266
535--558
(1970)
http://www.jstor.org/view/00804614/ap000403/00a00010/0?frame=noframe&userID=80683286@wisc.edu/01cc9933961923109e07138f6&dpi=3&config=jstor
Roberts.PTRSLA.1972
Kinematic Dynamo Models
Roberts
ptrsla
272
663--703
(1972)
http://links.jstor.org/sici?sici=0080-4614%2819720817%29272%3A1230%3C663%3AKDM%3E2.0.CO%3B2-4
Roberts.Paris.1971
Dynamo theory of geomagnetism (Geomagnetism theory of dynamos in homogeneous fluid masses, considering {R}ikitake self reversing, kinematic and hydromagnetic dynamo problems)
Roberts
123--131
(1971)
Roberts.RMP.2000
Geodynamo theory and simulations
Roberts and Glatzmaier
Rev. Mod. Phys.
72
(2000)
Geodynamo theory and simulations.pdf
http://link.aps.org/abstract/RMP/v72/p1081
Rogers.AJ.2006
Angular Momentum Transport by Gravity Waves in the Solar Interior
Rogers and Glatzmaier
Astro. Phys. J.
653
756--764
(2006)
Angular Momentum Transport by Gravity Waves0.pdf
http://dx.doi.org/10.1086/507259
10.1086/507259
We present self‐consistent numerical simulations of the Sun's convection zone and radiative interior using a two‐dimensional model of the solar equatorial plane. The background reference state is a one‐dimensional solar structure model. Turbulent convection in the outer convection zone continually excites gravity waves that propagate throughout the stable radiative interior and deposit their angular momentum. We find that angular velocity variations in the tachocline are driven by angular momentum transported by overshooting convective plumes rather than nonlinear interaction of waves. The mean flow in the tachocline is time dependent but not oscillatory in direction and not like a quasi‐biennial oscillation (QBO). Since the forcing in this shallow region cannot be described by simple linear waves, it is unlikely that the interaction of such waves is responsible for the solar cycle or the 1.3 yr oscillation. However, in the deep radiative interior, the interaction of low‐amplitude gravity waves, continually excited by the overshooting plumes, is responsible for the angular velocity deviations observed there, which do resemble a very low amplitude QBO. Near the center of the model Sun the angular velocity deviation is about 2 orders of magnitude greater than that in the bulk of the radiative region and reverses its direction (prograde to retrograde or vice versa) in the opposite sense of the angular velocity deviations that occur in the tachocline. Our simulations thus demonstrate how angular velocity variations in the solar core are linked to those in the tachocline, which themselves are driven by convective overshooting.
Rosner.APJ.2001
On the C/O Enrichment of Nova Ejecta
Rosner and Alexakis and Young and Truran and Hillebrandt
Astrophys. J.
562
L177--L179
(2001)
On the C-O Enrichment of Nova Ejecta.pdf
10.1086/338327
Using the results of recent work in shear instabilities in stratified fluids, we show that the resonant interaction between large-scale flows in the accreted H/He envelope of white dwarf stars and interfacial gravity waves can mix the star's envelope with the white dwarf's surface material, leading to the enhancement of the envelope's C/O abundance to levels required by extant models for nova outbursts.
Rosner.book.2005
Mixing at the surface of white dwarf stars
Rosner and Alexakis
Fluid Dynamics and Dynamos in Astrophysics and Geophysics
63--82
(2005)
http://books.google.com/books?hl=en&lr=&id=qC1KvSxl_PIC&oi=fnd&pg=PA63&ots=GTv3jylzUh&sig=qG30agGgOcBGfKTjxNP1-qNVeLI#PPA63,M1
Rossby.JMR.1939
Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action
Rossby and others
J. Mar. Res
2
38--55
(1939)
Relation between variations in the intensity of the zonal.pdf
Rudiger
The Magnetic Universe: Geophysical and Astrophysical Dynamo Theory
R\"{u}diger and Hollerbach
(2004)
Rudiger.AA.2001
{MHD instability in differentially-rotating cylindric flows}
Rüdiger and Zhang
Astron. Astrophys.
378
302--308
(2001)
Rudiger.AN.2005
{The stability of MHD Taylor-Couette flow with current-free spiral magnetic fields between conducting cylinders}
Rüdiger and Hollerbach and Schultz and Shalybkov
Astronomische Nachrichten
326
409--413
(2005)
The stability of MHD Taylor-Couette flow with current-free.pdf
Rudiger.AN.2007
The azimuthal magnetorotational instability (AMRI)
G. R\"{u}diger, R. Hollerbach
Astron. Nachr.
328
1158-1161
(2007)
The azimuthal magnetorotational instability (AMRI).pdf
http://dx.doi.org/10.1002/asna.200710852
We consider the flow of an electrically conducting fluid between differentially rotating cylinders, in the presence of an externally imposed current-free toroidal field B0(Rin/R) ê . It is known that the classical, axisymmetric magnetorotational instability does not exist for such a purely toroidal imposed field.We show here that a nonaxisymmetric magnetorotational instability does exist, having properties very similar to the axisymmetric magnetorotational instability in the presence of an axial field. In the nonlinear regime the magnetic energy of the perturbances is shifted (in the sense of an inverse cascade) to the axisymmetric mode rather than to the modes with m > 1.
Rudiger.APJ.2006
{The Traveling-Wave MRI in Cylindrical Taylor-Couette Flow: Comparing Wavelengths and Speeds in Theory and Experiment}
Rüdiger and Hollerbach and Stefani and Gundrum and Gerbeth and Rosner
The Astrophysical Journal
649
L145--L147
(2006)
Ruzmaikin.APSS.1982
Spectrum of the galactic magnetic fields
Ruzmaikin and Shukurov
apss
82
397--407
(1982)
Ryu.AJ.1992
Convective instability in differentially rotating disks
Ryu and Goodman
Astrophysical Journal
388
438--450
(1992)
Convective instability in differentially rotating disks.pdf
http://adsabs.harvard.edu/abs/1992ApJ...388..438R
A normal mode analysis for nonaxisymmetric perturbations in a thin, differentially rotating disk with a vertical structure that is isothermal and convectively unstable is performed. The vertical gravity is assumed to be external and constant. The perturbation scale is assumed to be much shorter than the radius of the disk but comparable to or less than the thickness. The initial value problem is formulated in shearing coordinates. Dispersion relations are obtained for the three limiting cases of zero shear, axisymmetric perturbations, and small radial wavelengths. The full effects of shear are studied by integrating numerically the initial value problem. Nonaxisymmetric local Fourier modes are found to have a radial wavenumber that increases linearly with time in proportion to the shear times the azimuthal wavenumber. While Coriolis forces exert stabilizing effects on the convective modes, reducing their growth rate and the range of unstable wavelengths, shear has destablizing effects inasmuch as it reduces the epicyclic frequency at a given angular velocity. In a Keplerian disk, perturbations with azimuthal wavelengths about 2 times smaller than vertical wavelengths grow exponentially.
Saleem.PL.2008
Angular momentum transport produced by shear flow driven drift waves in a collisional magnetoplasma
Saleem and Shukla and Eliasson
Phys. Lett. A
372
6648--6649
(2008)
Angular momentum transport produced by shear.pdf
http://www.sciencedirect.com/science/article/B6TVM-4TDVM9C-5/2/e7276caf4577f825198e716676abab14
10.1016/j.physleta.2008.08.075
Sano.AJ.1999
Magnetorotational Instability in Protoplanetary Disks. I. On the Global Stability of Weakly Ionized Disks with Ohmic Dissipation
Sano and Miyama
The Astrophysical Journal
515
776-786
(1999)
Magnetorotational Instability in Protoplanetary Disks. I. On the Global.pdf
http://www.journals.uchicago.edu/doi/abs/10.1086/307063
We investigate the stability of uniformly magnetized accretion disks, including the effect of ohmic dissipation. The growth of axisymmetric local and global modes is examined using linear perturbation theory. A simple local analysis shows that the dissipation process generally suppresses the growth of magnetorotational instability when the magnetic Reynolds number is less than unity. The characteristic length scale of unstable modes becomes longer than that of the ideal MHD case, and its unstable growth rate is inversely proportional to the magnetic diffusivity. We perform a global linear analysis in which the vertical structure of the disk is considered. The growth rate of the magnetorotational instability is obtained by solving eigen equations numerically. We find that the conditions for existing unstable global modes are $\beta _{c}\gtrsim 1$ and $\beta _{c}R_{mc}\gtrsim 1$ , where $\beta _{c}$ and $R_{mc}$ are the plasma beta value and the magnetic Reynolds number defined at the midplane of the disk. The global stability criteria are approximately given by whether the minimum unstable wavelength expected by the local analysis would be shorter than the scale height of the disk or not. We also find unstable modes whose eigenfunctions of the perturbed velocities have amplitude localized near the surface layer of the disk. These unstable modes indicate layered accretion in the nonlinear regime. We apply the results of linear analysis to protoplanetary disks. For the case of the minimum-mass solar nebula, the magnetorotational instability occurs at the region farther out than 15 AU. This result suggests nonsteady accretion onto a central star in protoplanetary disks.
Sano.AJ.2004
Angular Momentum Transport by Magnetohydrodynamic Turbulence in Accretion Disks: Gas Pressure Dependence of the Saturation Level of the Magnetorotational Instability
Sano and Inutsuka and Turner and Stone
Astro. Phys. J.
605
321--339
(2004)
Angular Momentum Transport by Magnetohydrodynamic Turbulence.pdf
http://dx.doi.org/10.1086/382184
The saturation level of the magnetorotational instability (MRI) is investigated using three‐dimensional MHD simulations. The shearing box approximation is adopted and the vertical component of gravity is ignored, so that the evolution of the MRI is followed in a small local part of the disk. We focus on the dependence of the saturation level of the stress on the gas pressure, which is a key assumption in the standard αdisk model. From our numerical experiments we find that there is a weak power‐law relation between the saturation level of the Maxwell stress and the gas pressure in the nonlinear regime; the higher the gas pressure, the larger the stress. Although the power‐law index depends slightly on the initial field geometry, the relationship between stress and gas pressure is independent of the initial field strength and is unaffected by ohmic dissipation if the magnetic Reynolds number is at least 10. The relationship is the same in adiabatic calculations, where pressure increases over time, and nearly isothermal calculations, where pressure varies little with time. Over the entire region of parameter space explored, turbulence driven by the MRI has many characteristic ratios such as that of the Maxwell stress to the magnetic pressure. We also find that the amplitudes of the spatial fluctuations in density and the time variability in the stress are characterized by the ratio of magnetic pressure to gas pressure in the nonlinear regime. Our numerical results are qualitatively consistent with an idea that the saturation level of the MRI is determined by a balance between the growth of the MRI and the dissipation of the field through reconnection. The quantitative interpretation of the pressure‐stress relation, however, may require advances in the theoretical understanding of nonsteady magnetic reconnection.
Saric.ARFM.1994
{Gortler vortices}
Saric
Annu. Rev. Fluid Mech.
26
379--409
(1994)
Gortler vortices.pdf
http://arjournals.annualreviews.org/doi/abs/10.1146/annurev.fl.26.010194.002115
10.1146/annurev.fl.26.010194.002115
Sarson.GAFD.1998
Convection driven geodynamo models of varying Ekman number
Sarson and Jones and Longbottom
gafd
88
225--259
(1998)
Sarson.PEPI.1997
The influence of boundary region heterogeneities on the geodynamo
Sarson and Jones and Longbottom
pepi
101
13--32
(1997)
Sarson.PEPI.1999
A convection driven geodynamo reversal model
Sarson and Jones
pepi
111
3--20
(1999)
Sarson.PTRSLA.2000
Reversal Models from Dynamo Calculations
Sarson
ptrsla
358
921--942
(2000)
http://links.jstor.org/sici?sici=1364-503X%2820000315%29358%3A1768%3C921%3ARMFDC%3E2.0.CO%3B2-C
Sarson.Science.1997
Magnetoconvection dynamos and the magnetic fields of {I}o and {G}anymede
Sarson and Jones
science
276
1106--1108
(1997)
Sarson.Thesis.1994
Kinematic Dynamo Calculations for Geomagnetism
Sarson
(1994)
Savelsberg.PRL.2008
{Turbulence of a Free Surface}
Savelsberg and van de Water
Phys. Rev. Lett.
100
34501
(2008)
Turbulence of a Free Surface.pdf
Schaeffer.EPSL.2006
Quasi-geostrophic kinematic dynamos at low magnetic Prandtl number
Schaeffer and Cardin
Earth and Planetary Science Letters
245
595--604
(2006)
Quasi-geostrophic kinematic dynamos at low magnetic Prandtl.pdf
http://www.sciencedirect.com/science/article/B6V61-4JVT1TH-1/2/62aaa0e42eaa284005f14a67157641a1
Rapidly rotating spherical kinematic dynamos at very low Ekman and Prandtl numbers are computed using the combination of a quasi-geostrophic (QG) model for the velocity field and a classical spectral 3D code for the magnetic field. The QG flow is computed in the equatorial plane of the sphere; it corresponds to Rossby wave instabilities of a geostrophic internal shear layer produced by differential rotation. The induction equation is computed in the whole sphere after the QG flow has been expanded along the rotation axis. Differential rotation and Rossby wave propagation are the key ingredients of this dynamo which can be interpreted in terms of Parker-Ω dynamo. Taking into account the quasi-geostrophy of the velocity field enables us to increase time and space resolution to compute the dynamics. For the first time, we report on numerical dynamos with very low Ekman numbers (10− 8). Because the magnetic and velocity fields are computed on different grids, we compute dynamos for very low magnetic Prandtl numbers exhibiting a scale separation between magnetic and velocity field. These dynamos are asymptotically close to rapidly rotating, metallic planetary cores.
Schartman.MHD.2006
The {P}rinceton Magnetorotational Instability Experiment
Schartman and Ji and Burin and Raftopoulos and Cutler and Heitzenroeder and Liu and Goodman and Stone and Kageyama
(2005)
Schartman.RSI.2009
Development of a Couette--Taylor flow device with active minimization of secondary circulation
Schartman and Ji and Burin
Rev. Sci. Instr.
80
024501--8
(2009)
Development of a Couette--Taylor flow device with.pdf
http://link.aip.org/link/?RSI/80/024501/1
A novel Taylor--Couette experiment has been developed to produce rotating shear flows for the study of hydrodynamic and magnetohydrodynamic instabilities which are believed to drive angular momentum transport in astrophysical accretion disks. High speed, concentric, corotating cylinders generate the flow where the height of the cylinders is twice the radial gap width. Ekman pumping is controlled and minimized by splitting the vertical boundaries into pairs of nested, differentially rotating rings. The end rings and cylinders comprise four independently driven rotating components which provide flexibility in developing flow profiles. The working fluids of the experiment are water, a water-glycerol mix, or a liquid gallium alloy. The mechanical complexity of the apparatus and large dynamic pressures generated by high speed operation with the gallium alloy presented unique challenges. The mechanical implementation of the experiment and some representative results obtained with laser Doppler velocimetry in water are discussed.
Schartman.Thesis.2008
Laboratory Study of Angular Momentum Transport in a Rotating Shear Flow
Schartman
(2008)
Laboratory Study of Angular Momentum Transport.pdf
http://mri.pppl.gov/schartman_thesis.pdf
The MagnetoRotational Instability (MRI) is widely accepted to be responsible for
the angular momentum transport in accretion disks which power some of the
most luminous objects in the universe. Conditions for instability to the MRI in
ideal MHD are: 1) an angular velocity which decreases with radius and 2) a
weak ambient magnetic field which allows the exchange of momentum between
radially-separated fluid elements. The MRI has not been conclusively detected in
the laboratory. Subcritical Hydrodynamic Instabilities have also received renewed
interest for application to cool circumstellar disks which may be too poorly ionized
to generate the MRI. Reports of purely hydrodynamic turbulence in subcritical
flows lack transport measurements to support the hypothesis that angular velocity
shear undergoes a spontaneous transition. A small aspect-ratio, wide gap circular-
Couette experiment capable of operation at Reynolds number in excess of 106 is
constructed to investigate these two mechanisms of angular momentum transport.
The apparatus consists of two concentric co-rotating cylinders. To minimize
the effect of the cylinder end caps, they are divided into nested differentially
rotatable rings. Water and a water-glycerol mix are used as working fluids to
study angular momentum transport in quasi-Keplerian flows and its scaling with
Reynolds number. When the end rings speeds are optimized, large-scale advective
transport due to the vertical boundaries is eliminated. The resulting flow is an
excellent approximation to the ideal circular-Couette profile. Measurement of the
r − φ component of the Reynolds stress using Laser Doppler Velocimetry shows no
indication of a subcritical instability. Pure hydrodynamic turbulence is an unlikely
mechanism to transport angular momentum in accretion disks.
Schekochihin.APJ.2005
{The Onset of a Small-Scale Turbulent Dynamo at Low Magnetic Prandtl Numbers}
{Schekochihin} and {Haugen} and {Brandenburg} and {Cowley} and {Maron} and {McWilliams}
apjl
625
L115-L118
(2005)
The Onset of a Small-Scale Turbulent Dynamo at Low Magnetic.pdf
10.1086/431214
We study numerically the dependence of the critical magnetic Reynolds number for the turbulent small-scale dynamo on the hydrodynamic Reynolds number . The turbulence is statistically homogeneous, isotropic, and mirror-symmetric. We are interested in the regime of low magnetic Prandtl number , which is relevant for stellar convective zones, protostellar disks, and laboratory liquid-metal experiments. The two asymptotic possibilities are as (a small-scale dynamo exists at low ) or as (no small-scale dynamo exists at low ). Results obtained in two independent sets of simulations of MHD turbulence using grid and spectral codes are brought together and found to be in quantitative agreement. We find that at currently accessible resolutions, grows with with no sign of approaching a constant limit. We reach the maximum values of for . By comparing simulations with Laplacian viscosity, fourth-, sixth-, and eighth-order hyperviscosity, and Smagorinsky large-eddy viscosity, we find that is not sensitive to the particular form of the viscous cutoff. This work represents a significant extension of the studies previously published by Schekochihin et al. (2004a) and Haugen et al. (2004a) and the first detailed scan of the numerically accessible part of the stability curve .
Schekochihin.PRL.2004A
{Critical Magnetic Prandtl Number for Small-Scale Dynamo}
Schekochihin and Cowley and Maron and McWilliams
prl
92
054502
(2004)
Critical Magnetic Prandtl Number for Small-Scale.pdf
http://link.aps.org/abstract/PRL/v92/e054502
We report a series of numerical simulations showing that the critical magnetic Reynolds number Rmc for the nonhelical small-scale dynamo depends on the Reynolds number Re. Namely, the dynamo is shut down if the magnetic Prandtl number Prm=Rm/Re is less than some critical value Prm,c≲1 even for Rm for which dynamo exists at Prm≥1. We argue that, in the limit of Re→∞, a finite Prm,c may exist. The second possibility is that Prm,c→0 as Re→∞, while Rmc tends to a very large constant value inaccessible at current resolutions. If there is a finite Prm,c, the dynamo is sustainable only if magnetic fields can exist at scales smaller than the flow scale, i.e., it is always effectively a large-Prm dynamo. If there is a finite Rmc, our results provide a lower bound: Rmc≳220 for Prm≤1/8. This is larger than Rm in many planets and in all liquid-metal experiments.
Schekochihin.PRL.2004B
Self-Similar Turbulent Dynamo
Schekochihin and Cowley and Maron and McWilliams
prl
92
064501
(2004)
Self-Similar Turbulent Dynamo.pdf
http://link.aps.org/abstract/PRL/v92/e064501
The amplification of magnetic fields in a highly conducting fluid is studied numerically. During growth, the magnetic field is spatially intermittent: it does not uniformly fill the volume, but is concentrated in long thin folded structures. Contrary to a commonly held view, intermittency of the folded field does not increase indefinitely throughout the growth stage if diffusion is present. Instead, as we show, the probability-density function (PDF) of the field-strength becomes self-similar. The normalized moments increase with magnetic Prandtl number in a powerlike fashion. We argue that the self-similarity is to be expected with a finite flow scale and system size. In the nonlinear saturated state, intermittency is reduced and the PDF is exponential. Parallels are noted with self-similar behavior recently observed for passive-scalar mixing and for map dynamos.
Schmitt.JFM.2008
{Rotating spherical Couette flow in a dipolar magnetic field: experimental study of magneto-inertial waves}
Schmitt and Alboussi{\v{c}}re and Brito and Cardin and Gagni{\v{c}}re and Jault and Nataf
J. Fluid Mech.
604
175--197
(2008)
Rotating spherical Couette flow in a dipolar.pdf
10.1017/S0022112008001298
The magnetostrophic regime, in which Lorentz and Coriolis forces are in balance, has been investigated in a rapidly rotating spherical Couette flow experiment. The spherical shell is filled with liquid sodium and permeated by a strong imposed dipolar magnetic field. Azimuthally travelling hydromagnetic waves have been put in evidence through a detailed analysis of electric potential differences measured on the outer sphere, and their properties have been determined. Several types of wave have been identified depending on the relative rotation rates of the inner and outer spheres: they differ by their dispersion relation and by their selection of azimuthal wavenumbers. In addition, these waves constitute the largest contribution to the observed fluctuations, and all of them travel in the retrograde direction in the frame of reference bound to the fluid. We identify these waves as magneto-inertial waves by virtue of the close proximity of the magnetic and inertial characteristic time scales of relevance in our experiment.
Schou.AJ.1998
Helioseismic studies of differential rotation in the solar envelope by the Solar Oscillations Investigation using the Michelson Doppler Imager
Schou and Antia and Basu and Bogart and Bush and Chitre and Christensen-Dalsgaard and Di Mauro and Dziembowski and Eff-Darwich
aj
505
390--417
(1998)
Schubert.Nature.1996
The magnetic field and internal structure of {G}anymede
Schubert and Zhang and Kivelson and Anderson
nature
384
544--545
(1996)
Schuster.PPSLA.1912
A Critical Examination of the Possible Causes of Terrestrial Magnetism
Schuster
ppsla
24
121--137
(1912)
Schwarzschild.PT.2006
Turbulent liquid-sodium flow induces magnetic dipole in a laboratory analogue of the geodynamo
Schwarzschild
Phys. Today
59
13
(2006)
http://www.physicstoday.org/vol-59/iss-2/p13.shtml
Scott
The Bullard-Gellman dynamo: Appendix
Scott
586--602
(1969)
Scott.PFB.1990
Correlations of heat and momentum transport in the {TFTR} tokamak
Scott and Arunasalam and Barnes and Bell and Bitter and Boivin and Bretz and Budny and Bush and Cavallo and Chu and Cohen and Colestock and Davis and Dimock and Dylla and Efthimion and Erhrardt and Fonck and Fredrickson and Furth and Goldston and Greene and Grek and Grisham and Hammett and Hawryluk and Hendel and Hill and Hinnov and Hoffman and Hosea and Howell and Hsuan and Hulse and Jaehnig and Janos and Jassby and Jobes and Johnson and Johnson and Kaita and Kieras-Phillips and Kilpatrick and LaMarche and LeBlanc and Little and Manos and Mansfield and Mazzucato and McCarthy and McCune and McGuire and McNeill and Meade and Medley and Mikkelsen and Motley and Mueller and Murphy and Nagayama and Nazakian and Owens and Park and Ramsey and Redi and Roquemore and Rutherford and Schilling and Schivell and Schmidt and Stevens and Stratton and Stodiek and Synakowski and Tang and Taylor and Timberlake and Towner and Ulrickson and von Goeler and Wieland and Williams and Wilson and Wong and Yoshikawa and Young and Zarnstorff and Zweben
Phys. Fluids B
2
1300--1305
(1990)
Correlations of heat and momentum transport in the TFTR.pdf
10.1063/1.859545
Measurements of the toroidal rotation speed vphi(r) driven by neutral beam injection in tokamak plasmas and, in particular, simultaneous profile measurements of vphi, Ti, Te, and ne, have provided new insights into the nature of anomalous transport in tokamaks. Low-recycling plasmas heated with unidirectional neutral beam injection exhibit a strong correlation among the local diffusivities, chiphi[approximately-equal-to]chii>chie. Recent measurements have confirmed similar behavior in broad-density L-mode plasmas. These results are consistent with the conjecture that electrostatic turbulence is the dominant transport mechanism in the tokamak fusion test reactor tokamak (TFTR) [Phys. Rev. Lett. 58, 1004 (1987)], and are inconsistent with predictions both from test-particle models of strong magnetic turbulence and from ripple transport. Toroidal rotation speed measurements in peaked-density TFTR ``supershots'' with partially unbalanced beam injection indicate that momentum transport decreases as the density profile becomes more peaked. In high-temperature, peaked-density plasmas the observed gradient scale length parameter etatoti=d ln Ti/d ln ne correlates reasonably well with predictions of the threshold for exciting ion-temperature-gradient-driven turbulence (ITGDT), as would be expected for plasmas at marginal stability with respect to this strong transport mechanism. In L-mode plasmas where ITGDT is expected to be too weak to enforce marginal stability, etatoti exceeds this threshold considerably. However, preliminary experiments have failed to observe a significant increase in ion heat transport when etatoti was rapidly forced above etac (the threshold for exciting ITGDT) using a perturbative particle source, as would have been expected for a plasma at marginal stability.
Shaing.NF.2003
Plasma and momentum transport processes in the vicinity of a magnetic island in a tokamak
Shaing and Hegna and Callen and Houlberg
nf
43
258--261
(2003)
Shercliff.JFM.1969
{Anisotropic surface waves under a vertical magnetic force}
Shercliff
J. Fluid Mech.
38
353--364
(1969)
Anisotropic surface waves under a vertical.pdf
10.1017/S0022112069000218
Shew.PEPI.2005
Liquid sodium model of geophysical core convection
Shew and Lathrop
Physics of The Earth and Planetary Interiors
153
136--149
(2005)
Liquid sodium model of geophysical core.pdf
http://www.sciencedirect.com/science/article/B6V6S-4HG6HD8-2/2/836c64eedb588cc592c495182370a5a4
Convective motions in Earth's outer core are responsible for the generation of the geomagnetic field. We present liquid sodium convection experiments in a spherical vessel, designed to model the convective state of planetary cores such as the Earth's. Heat transfer, azimuthal fluid velocities, and properties of temperature fluctuations were measured for different rotation rates and temperature drops across the convecting sodium. We observed small-scale convective motions with strong, large-scale azimuthal winds and developed turbulence despite the fact that convective heat transport was weak and the temperature profile was close to diffusive. In the context of Earth's outer core, our observations suggest models which imply a thermal Rayleigh number Ra≈6×1023 and a convective velocity near 2×10−4 m/s. Also, the energy spectrum of outer core may exhibit important structure down to length and time scales of 1 km and 30 days. Furthermore, we calculate an estimate of Ohmic dissipation, 0.1 TW, in the core based on the shape of experimentally observed power spectra.
Shpilrain.1985
Dynamic and Kinematic Viscosity of Liquid Alkali Metals
Shpil'rain and Yakimovich and Fomin and Skovorodjko and Mozgovoi
(1985)
Shpilrain.1985A
Dynamic and Kinematic Viscosity of Liquid Alkali Metals
Shpil'rain and Yakimovich and Fomin and Skovorodjko and Mozgovoi
(1985)
Shpilrain.1985B
Density and Thermal Expansion of Liquid Alkali Metals
Shpil'rain and Yakimovich and Fomin and Skovorodjko and Mozgovoi
(1985)
Shraiman.PR.1990
Heat transport in high-Rayleigh-number convection
Shraiman and Siggia
Phys. Rev. A
42
(1990)
Heat transport in high-Rayleigh-number convection.pdf
http://link.aps.org/abstract/PRA/v42/p3650
The heat flux (Nusselt number) as a function of Rayleigh number, NNu≊0.3NRa2/7, is deduced from the presence of a mean flow and the nesting of the thermal boundary layer within the viscous one. The numerical coefficients are obtained from those known empirically for turbulent boundary layers. The consistency of our assumptions as a function of Prandtl number limits this regime to (107--108)NPr5/3≲NRa≲ (1013--1015)NPr4. The Bolgiano-Obukhov k-7/5 spectrum for the temperature fluctuations is inconsistent with a simple scaling treatment of the equations.
Siggia.ARFM.1994
High Rayleigh Number Convection
Siggia
Annu. Rev. Fluid Mech.
26
137-168
(1994)
High Rayleigh Number Convection.pdf
http://arjournals.annualreviews.org/doi/abs/10.1146/annurev.fl.26.010194.001033
Sisan.PEPI.2003
Lorentz force effects in magneto-turbulence
Sisan and Shew and Lathrop
Phys. Earth Planetary Inter.
135
137--159
(2003)
Lorentz force effects in magneto-turbulence.pdf
http://www.sciencedirect.com/science/article/B6V6S-47XWMGY-1/2/5314c871f23912b13b1ad7d40f0642e9
We experimentally characterize magnetic field fluctuations in a strongly turbulent flow of liquid sodium in the presence of a large externally applied field. We reach high interaction parameter (up to N=17) for moderate magnetic Reynolds number (up to Rem=18), a previously unexplored parameter range for liquid metal flows. As the interaction parameter (i.e. the ratio of Lorentz to inertial forces) is increased, the system passes through distinct regimes, which we classify. We find that for certain ranges of the applied magnetic field, particularly at high values, the induced magnetic field exhibits large, coherent oscillations. Spatial structure in these induced field oscillations suggests the formation of non-axisymmetric vortices that precess at a fraction of the impeller rotation rate. We also investigate the effect of rough versus smooth boundaries and relate these results to topographic core-mantle coupling in the Earth.
Sisan.PRL.2004
Experimental Observation and Characterization of the Magnetorotational Instability
Sisan and Mujica and Tillotson and Huang and Dorland and Hassam and Antonsen and Lathrop
Phys. Rev. Lett.
93
114502
(2004)
Experimental Observation and Characterization of the Magnetorotational Instability.pdf
http://link.aps.org/abstract/PRL/v93/e114502
10.1103/PhysRevLett.93.114502
Differential rotation occurs in conducting flows in accretion disks and planetary cores. In such systems, the magnetorotational instability can arise from coupling Lorentz and centrifugal forces to cause large radial angular momentum fluxes. We present the first experimental observation of the magnetorotational instability. Our system consists of liquid sodium between differentially rotating spheres, with an imposed coaxial magnetic field. We characterize the observed patterns, dynamics, and torque increases, and establish that this instability can occur from a hydrodynamic turbulent background.
Smith.PF.1999
Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence
Smith and Waleffe
Phys. Fluids
11
1608--1622
(1999)
Transfer of energy to two-dimensional large scales.pdf
http://link.aip.org/link/?PHF/11/1608/1
Smolentsev.FED.2002
{Experimental study of turbulent supercritical open channel water flow as applied to the CLiFF concept}
Smolentsev and Freeze and Morley and Abdou
Fusion Eng. \& Design
63
397--403
(2002)
Experimental study of turbulent supercritical open.pdf
10.1016/S0920-3796(02)00121-7
An experimental study of turbulent open channel water flows was conducted that simulated basic features of the flow of molten salt in the convective liquid flow first-wall (CLiFF) concept, which is a part of the Advanced Power Extraction (APEX) study. Unlike many other studies of open channel flows, the present one concentrates on a supercritical flow regime, in which surface waviness and wave--turbulence interaction are the most important processes that determine the heat transfer rate in CLiFF flows. The current study covers the Reynolds number and Froude number range of 1×104--6×104 and 150--250, respectively, with a fixed chute inclination angle of 30$\,^{\circ}$. The statistical characteristics of the wavy interface were obtained with an ultrasound transducer. A spectral analysis of the oscillating flow thickness shows that a major part of the spectrum is presented by long finite-amplitude waves (f=10--50 Hz), which carry a significant part of the volumetric flux. Based on dye technique observations, short waves are mostly responsible for mixing the liquid at the surface. The surface waviness can be characterized by a parameter built through the mean flow thickness, h, and its standard deviation (S.D.), σ, as 0.5σ/h, which is almost constant, 0.1, in all experiments. The mean flow thickness variations are predicted well with the `K--var epsilon' model of turbulence [Int. J. Eng. Sci. 40/6 (2002) 693], but the fluctuations are not resolved. Thermal images of the free surface measured by an infrared (IR) camera are very non-uniform and show the `strike' structures in the form of elongated strips of `hotter' and `cooler' liquid. The present observations are the first steps to better understanding and quantitative predictions of liquid wall flows in the CLiFF design.
Smolentsev.FED.2004
{Thermofluid modeling and experiments for free surface flows of low-conductivity fluid in fusion systems}
Smolentsev and Morley and Freeze and Miraghaie and Nave and Banerjee and Ying and Abdou
Fusion Eng. \& Design
72
63--81
(2004)
Thermofluid modeling and experiments for free surface.pdf
The paper summarizes results of experimental and theoretical studies related to the flow of liquids with a free surface and poor electrical and thermal conductivity, such as molten salts, under conditions relevant to fusion energy systems. These results have been obtained over last several years when developing the liquid wall concept as a part of the APEX project [M.A. Abdou, The APEX TEAM, On the exploration of innovative concepts for fusion chamber technology, Fusion Eng. Des. 54 (2001) 181--247]. As a theoretical tool a modified K--var epsilon model of turbulence coupled with the Navier--Stokes equations written in the thin-shear-layer approximation is used for studying wavy, turbulent flows in a spanwise magnetic field. The experimental part covers current results for supercritical flows in regimes transitional from ``weak'' to ``strong'' turbulence, which are expected to occur in the reference liquid wall flows. The paper also describes on-going work on novel schemes of heat transfer promotion and current directions for direct numerical simulation.
Smolentsev.IJES.2002
{Application of the "K--$\varepsilon$" model to open channel flows in a magnetic field}
Smolentsev and Abdou and Morley and Ying and Kunugi
Int. J. Eng. Sci.
40
693--711
(2002)
Application of the "K--$\varepsilon$" model to open channel.pdf
In magnetohydrodynamic (MHD) flows turbulence reduction occurs due to the Joule dissipation. It results in heat transfer degradation. In open channel flows, heat transfer degradation is also caused by the turbulence redistribution near the free surface. Both effects can be significant in fusion applications with low-conductivity fluids such as molten salts. In the present study, the ``K--var epsilon'' model equations for turbulent flows and the free surface boundary condition are adjusted with taking into account MHD effects. Different orientations of the magnetic field, perpendicular and parallel to the main flow, have been considered. The model coefficients have been tuned by a computer optimization using available experimental data for the friction factor. The effect of free surface heat transfer degradation due to the turbulence redistribution has been implemented through the variation of the turbulent Prandtl number. As an example, the model is used for the analysis of a turbulent MHD flow down an inclined chute with the heat flux applied to the free surface.
Spells.PPS.1936
{The determination of the viscosity of liquid gallium over an extended nrange of temperature}
Spells
pps
48
299--311
(1936)
Spence.APS.2008
Simulations of waves in magnetised spherical Couette flow
Spence and Reuter
Bull. Am. Phys. Soc.
53
299
(2008)
http://meetings.aps.org/Meeting/DPP08/Event/89187
Spence.PRL.2006
Observation of a Turbulence-Induced Large Scale Magnetic Field
Spence and Nornberg and Jacobson and Kendrick and Forest
prl
96
055002
(2006)
10.1103/PhysRevLett.96.055002
Spence.PRL.2007
Turbulent Diamagnetism in Flowing Liquid Sodium
Spence and Nornberg and Jacobson and Parada and Taylor and Kendrick and Forest
prl
(2007)
Spence.Thesis.2006
{Experimental observation of fluctuation-driven mean magnetic fields in the Madison Dynamo Experiment}
Spence
(2006)
Spitkovsky.APJ.2002
Propagation of Thermonuclear Flames on Rapidly Rotating Neutron Stars: Extreme Weather during Type I X-Ray Bursts
Spitkovsky and Levin and Ushomirsky
Astrophys. J.
566
1018-1038
(2002)
Propagation of Thermonuclear Flames on Rapidly Rotating.pdf
http://www.journals.uchicago.edu/doi/abs/10.1086/338040
10.1086/338040
We analyze the global hydrodynamic flow in the ocean of an accreting, rapidly rotating, nonmagnetic neutron star in a low-mass X-ray binary during a type I X-ray burst. We use both analytical arguments and numerical simulations of simplified models for ocean burning. Our analysis extends previous work by taking into account the rapid rotation of the star and the lift-up of the burning ocean during the burst. We find a new regime for the spreading of a nuclear burning front, where the flame is carried along a coherent shear flow across the front. If turbulent viscosity is weak, the speed of flame propagation is km s−1, where h is the scale height of the burning ocean, g is the local gravitational acceleration, tn is the timescale for fast nuclear burning during the burst, and f is the Coriolis parameter, i.e., twice the local vertical component of the spin vector. If turbulent viscosity is dynamically important, the flame speed increases and reaches the maximum value, km s−1, when the eddy overturn frequency is comparable to the Coriolis parameter f. We show that, as a result of rotationally reduced gravity, the thermonuclear runaway which ignites the ocean is likely to begin on the equator. The equatorial belt is ignited at the beginning of the burst, and the flame then propagates from the equator to the poles. Inhomogeneous cooling (equator first, poles second) of the hot ashes drives strong zonal currents which may be unstable to the formation of Jupiter-type vortices; we conjecture that these vortices are responsible for coherent modulation of X-ray flux in the tails of some bursts. We consider the effect of strong zonal currents on the frequency of modulation of the X-ray flux and show that the large values of the frequency drifts observed in some bursts can be accounted for within our model combined with the model of homogeneous radial expansion. Additionally, if vortices or other inhomogeneities are trapped in the forward zonal flows around the propagating burning front, fast chirps with large frequency ranges (25-500 Hz) may be detectable during the burst rise. Finally, we argue that an MHD dynamo within the burning front can generate a small-scale magnetic field, which may enforce vertically rigid flow in the front's wake and can explain the coherence of oscillations in the burst tail.
Sreenivasan.2005
Structure and dynamics of the polar vortex in the {E}arth's core
Sreenivasan and Jones
()
Sreenivasan.GJI.2000
The role of inertia in the evolution of spherical dynamos
Sreenivasan and Jones
gji
(2000)
Sridhar.APJ.1994
{Toward a theory of interstellar turbulence. 1: Weak Alfvenic turbulence}
{Sridhar} and {Goldreich}
apj
432
612-621
(1994)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1994ApJ...432..612S&db_key=AST
10.1086/174600
Stacey.PP.2001
Momentum confinement in {DIII-D} shots with impurities
Stacy and Murakami
pp
8
4450--4454
(2001)
Stanley.EPSL.2005
Thin shell dynamo models consistent with Mercury's weak observed magnetic field
Stanley and Bloxham and Hutchinson and Zuber
epsl
234
27--38
(2005)
Stanley.Nature.2004
Convective-region geometry as the cause of Uranus' and Neptune's unusual magnetic fields
Stanley and Bloxham
nature
428
151--153
(2004)
Starrfield.MNRAS.1971
On the cause of the Nova outburst.
Starrfield
Mon. Not. R. Astron. Soc
152
307
(1971)
On the cause of the Nova outburst..pdf
A large number of models are evolved for thermonuclear runaways in the hydrogen-rich envelopes of 1.00-solar-mass carbon-oxygen white dwarfs. Models characterized by enhanced CNO abundances satisfy the observations of the common nova outburst, ejecting from 10 to the 27th to 10 to the 29th power g at velocities of 200 to 2400 km/s and kinetic energies of 10 to the 44th to 10 to the 45th power erg. The theoretical light curves are similar to the observed light curves of common novae during the early stages of the outbursts. Explanations are given for the continuous ejection of mass which is observed for long times after the initial outbursts, for the relationship between maximum magnitude and the decline to minimum, and for the constant luminosity phase of the outburst and the oval shapes of the ejected nebulae. The analysis is extended to models with extreme enhancements of C-12 and to models which include infalling material in the evolution. The extreme C-12 studies result in outbursts which reach near-supernova proportions, while the accretion models result in light curves which resemble observed light curves quite closely. The accretion studies also demonstrate the need for enhanced abundances.
Steenbeck.SPD.1968
Experimental Discovery of the Electromotive Force along the External Magnetic Field Induced by a Flow of Liquid Metal ($\alpha$-Effect)
Steenbeck and Kirko and Gailitis and Klyavinya and Krause and Laumanis and Lielausis
spd
13
443--445
(1968)
Steenbeck.ZNT.1966
The Generation of Stellar and Planetary Magnetic Fields by Turbulent Dynamo Action
Steenbeck and Krause
znt
21
1285-1296
(1966)
Stefani.2004
Inverse Problems in Magnetohydrodynamics: Theoretical and Experimental Aspects
Stefani and Gundrum and Gerbeth and G\"{u}nther and Xu
(2004)
Stefani.IP.1999
Velocity reconstruction in conducting fluids from magnetic field and electric potential measurements
Stefani and Gerbeth
ip
15
771--786
(1999)
Stefani.IP.2000
On the uniqueness of velocity reconstruction in conducting fluids from measurements of induced electromagnetic fields
Stefani and Gerbeth
ip
16
1--9
(2000)
Stefani.JP.2007
Experiments on the magnetorotational instability in helical magnetic fields
Stefani and Gundrum and Gerbeth and R\"udiger and Szklarski and Hollerbach
New J. Phys.
9
295--295
(2007)
Experiments on the magnetorotational instability in helical magnetic.pdf
10.1088/1367-2630/9/8/295
The magnetorotational instability (MRI) plays a key role in the formation of stars and black holes, by enabling outward angular momentum transport in accretion discs. The use of combined axial and azimuthal magnetic fields allows the investigation of this effect in liquid metal flows at moderate Reynolds and Hartmann numbers. A variety of experimental results is presented showing evidence for the occurrence of the MRI in a Taylor-Couette flow using the liquid metal alloy GaInSn.
Stefani.MST.2000
A contactless method for velocity reconstruction in electrically conducting fluids
Stefani and Gerbeth
mst
11
758--765
(2000)
Stefani.PRE.2004
Contactless inductive flow tomography
Stefani and Gundrum and Gerbeth
pre
70
056306
(2004)
Stefani.PRL.2006
{Experimental Evidence for Magnetorotational Instability in a Taylor-Couette Flow under the Influence of a Helical Magnetic Field}
Stefani and Gundrum and Gerbeth and Rüdiger and Schultz and Szklarski and Hollerbach
Phys. Rev Lett.
97
184502
(2006)
Experimental Evidence for Magnetorotational Instability in a Taylor-Couette.pdf
A recent Letter [R. Hollerbach and G. Ru ̈ diger, Phys. Rev. Lett. 95, 124501 (2005)] has shown that the threshold for the onset of the magnetorotational instability in a Taylor-Couette flow is dramatically reduced if both axial and azimuthal magnetic fields are imposed. In agreement with this prediction, we present results of a Taylor-Couette experiment with the liquid metal alloy GaInSn, showing evidence for the existence of the magnetorotational instability at Reynolds numbers of order 1000 and Hartmann numbers of order 10.
Stefani.Perm.2005
{Have we understood the Riga dynamo?}
Stefani and Gerbeth and Gailisis and Lielausis and Platacis
69
(2005)
http://pdd2005.icmm.ru/prog.htm
Stepanov.PRE.2006
Induction, helicity, and alpha effect in a toroidal screw flow of liquid gallium
Stepanov and Volk and Denisov and Frick and Noskov and Pinton
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
73
046310
(2006)
http://link.aps.org/abstract/PRE/v73/e046310
Stern.RG.2002
A millennium of geomagnetism
Stern
Rev. Geophys.
40
1--30
(2002)
10.1029/2000RG000097
Stieglitz.PF.2001
Experimental demonstration of a homogeneous two-scale dynamo
Stieglitz and M\"{u}ller
pf
13
561--564
(2001)
http://link.aip.org/link/?PHF/13/561/1
Stone.AJ.1996
Three--dimensional magnetohydrodynamic simulations of vertically stratified accretion disks
Stone and Hawley and Gammie and Balbus
aj
463
656--673
()
Stuart.PRSLA.1954
On the Stability of Viscous Flow between Parallel Plates in the Presence of a Co-Planar Magnetic Field
Stuart
prsla
221
189--206
(1954)
http://links.jstor.org/sici?sici=0080-4630%2819540121%29221%3A1145%3C189%3AOTSOVF%3E2.0.CO%3B2-U
Subramanian.PRL.1999
Unified Treatment of Small- and Large-Scale Dynamos in Helical Turbulence
Subramanian
prl
83
2957--2960
(1999)
Unified Treatment of Small- and Large-Scale Dynamos.pdf
10.1103/PhysRevLett.83.2957
Sweet.PP.2001
Blowout bifurcations and the onset of magnetic dynamo action
Sweet and Ott and Thomas M. Antonsen and Lathrop and Finn
pp
8
1944-1952
(2001)
10.1063/1.1342228
Sweet.PRE.2001
Blowout bifurcations and the onset of magnetic activity in turbulent dynamos
Sweet and Ott and Finn and Jr. and Lathrop
pre
63
066211
(2001)
10.1103/PhysRevE.63.066211
Szklarski.AN.2008
Boundary layer in the MRI experiment PROMISE
Szklarski and Gerbeth
Astronomische Nachrichten
329
667-674
(2008)
Boundary layer in the MRI experiment PROMISE0.pdf
http://dx.doi.org/10.1002/asna.200811019
10.1002/asna.200811019
One of the most convenient approaches to observe experimentally the magnetorotational instability (MRI) is to use a magnetized Taylor-Couette setup. The flow of liquid metal between two rotating, concentric cylinders can become unstable in the presence of an external magnetic field. One of the issues which should be addressed when designing such an experiment is the influence of plates enclosing the cylinders fromthe top and the bottom. In this paper we discuss properties of the boundary layer which arises near these plates. Our primary concern is the importance of this layer in the MRI experiment PROMISE.
Takeda.ETFS.1995
Velocity Profile Measurement by Ultrasound Doppler Method
Takeda
Exp. Thermal and Fluid Sci.
10
444--453
(1995)
Takeda.NED.1991
Development of an Ultrasound Velocity Profile Monitor
Takeda
Nuc. Eng. and Design
126
277--284
(1991)
Development of an Ultrasound Velocity Profile Monitor.pdf
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4D-4811010-1FS&_user=1082852&_coverDate=04%2F02%2F1991&_fmt=abstract&_orig=search&_cdi=5756&view=c&_acct=C000051401&_version=1&_urlVersion=0&_userid=1082852&md5=41daaf8144d8736dd6e1afcdeb172db6&ref=full
Tao.APJ.1998
Flux Separation in Stellar Magnetoconvection
Tao and Weiss and Brownjohn and Proctor
apj
496
L39-L42
(1998)
Tao.MNRAS.1998
{Flux expulsion by inhomogeneous turbulence}
Tao and Proctor and Weiss
mnras
300
907-914
(1998)
Tayler.MNRAS.1986
{A further uncertainty in the mixing length theory of convection in the structure of late-type stars}
{Tayler}
Mon. Not. R. Astron. Soc.
220
793-797
(1986)
A further uncertainty in the mixing length theory.pdf
Taylor.PP.2000
Relaxation revisited
Taylor
Phys. Plasmas
7
1623--1629
(2000)
Relaxation revisited.pdf
http://link.aip.org/link/?PHP/7/1623/1
10.1063/1.873984
Relaxation is the result of turbulence in a plasma that behaves essentially as an ideal conducting fluid, but has a small resistivity and viscosity. These small effects are locally enhanced by the turbulence and lead to reconnection of magnetic field lines. This destroys an infinity of topological constraints, leaving only the total magnetic helicity as a valid invariant. The plasma therefore rapidly reaches a specific state of minimum energy. This minimum energy "relaxed state" can be calculated from first principles and has many striking features. These depend on the topology of the system. They include spontaneous field reversal, symmetry-breaking and current limitation in toroidal pinches, and flux generation and flux amplification in Spheromaks. In addition the relaxed states can be controlled and maintained by injection of helicity from an external circuit. These features, and the profiles of the relaxed states themselves, have been verified in many laboratory experiments.
Taylor.PRSLA.1938
{The Spectrum of Turbulence}
{Taylor}
prsla
164
476-490
(1938)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1938RSPSA.164..476T&db_key=GEN
Tennekes_and_Lumley
A First Course in Turbulence
Tennekes and Lumley
(1972)
Terry.PRL.2002
Nonlinear Damping of Plasma Zonal Flows Excited by Inverse Spectral Transfer
Terry and Gatto and Baver
Phys. Rev. Lett.
89
(2002)
Nonlinear Damping of Plasma Zonal Flows.pdf
http://link.aps.org/abstract/PRL/v89/e205001
Plasma zonal-flow excitation and saturation in fluid electron-drift-wave turbulence are studied spectrally. The zonal flow is a spectral condensation onto the zero-frequency linear-wave structure. In the representation diagonalizing the wave coupling that dominates interactions at long wavelengths, nonlinear triad interactions involving zero-frequency waves are greatly enhanced. Zonal modes are excited on both unstable and purely stable eigenmode branches. Coupling to the latter introduces robust, finite amplitude-induced damping of zonal flows, providing saturation.
Terry.PRL.2004
Inverse Energy Transfer by Near-Resonant Interactions with a Damped-Wave Spectrum
Terry
Phys. Rev Lett.
93
(2004)
Inverse Energy Transfer by Near-Resonant Interactions.pdf
http://link.aps.org/abstract/PRL/v93/e235004
10.1103/PhysRevLett.93.235004
The interaction of long-wavelength anisotropic drift waves with the plasma turbulence of electron density advection is shown to produce the inverse energy transfer that condenses onto zonal modes, despite the expectation of forward transfer on the basis of nonconservation of enstrophy. Wave triads with an unstable wave and two waves of a separate, damped spectrum carry the transfer, provided they satisfy a near-resonance condition dependent on turbulence level and wave number.
Terry.RMP.2000
Suppression of turbulence and transport by sheared flow
Terry
rmp
72
000109
(2000)
Suppression of turbulence and transport by sheared flow.pdf
http://link.aps.org/doi/10.1103/RevModPhys.72.109
The role of stable shear flow in suppressing turbulence and turbulent transport in plasmas and neutral fluids is reviewed. Localized stable flow shear produces transport barriers whose extensive and highly successful utilization in fusion devices has made them the primary experimental technique for reducing and even eliminating the rapid turbulent losses of heat and particles that characterize fusion-grade plasmas. These transport barriers occur in different plasma regions with disparate physical properties and in a range of confining configurations, indicating a physical process of unusual universality. Flow shear suppresses turbulence by speeding up turbulent decorrelation. This is a robust feature of advection whenever the straining rate of stable mean flow shear exceeds the nonlinear decorrelation rate. Shear straining lowers correlation lengths in the direction of shear and reduces turbulent amplitudes. It also disrupts other processes that feed into or result from turbulence, including the linear instability of important collective modes, the transport-producing correlations between advecting fluid and advectants, and large-scale spatially connected avalanchelike transport events. In plasmas, regions of stable flow shear can be externally driven, but most frequently are created spontaneously in critical transitions between different plasma states. Shear suppression occurs in hydrodynamics and represents an extension of rapid-distortion theory to a long-time-scale nonlinear regime in two-dimensional stable shear flow. Examples from hydrodynamics include the emergence of coherent vortices in decaying two-dimensional Navier-Stokes turbulence and the reduction of turbulent transport in the stratosphere.
Thorpe.AR.2004
{Langmuir Circulation}
Thorpe
Annu. Rev. Fluid Mech.
36
55--79
(2004)
Langmuir Circulation.pdf
Tikhonov_and_Arsenin
Solutions of ill-posed problems
Tikhonov and Arsenin
(1977)
Tilgner.PF.2002
Numerical simulation of the onset of dynamo action in an experimental two-scale dynamo
Tilgner
pf
14
4092-4094
(2002)
http://link.aip.org/link/?PHF/14/4092/1
Tillotson.Thesis.2007
{Numerical Simulations of Magnetorotational Turbulence in the Laboratory}
Tillotson
(2007)
Numerical Simulations of Magnetorotational Turbulence in the Laboratory.pdf
http://hdl.handle.net/1903/7146
Tobias.APJ.2007
$\beta$‐Plane Magnetohydrodynamic Turbulence in the Solar Tachocline
Tobias and Diamond and Hughes
Astrophys. J. Lett.
667
L113-L116
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$\beta$‐Plane Magnetohydrodynamic Turbulence in the Solar Tachocline.pdf
http://www.journals.uchicago.edu/doi/full/10.1086/521978
10.1086/521978
This Letter discusses the role of a weak toroidal magnetic field in modifying the turbulent transport properties of stably stratified rotating turbulence in the tachocline. A local two‐dimensional β‐plane model is investigated numerically. In the absence of magnetic fields, nonlinear interactions of Rossby waves lead to the formation of strong mean zonal flows. However, the addition of even a very weak toroidal field suppresses the generation of mean flows. We argue that this has serious implications for angular momentum transport in the lower tachocline.
Urpin.AA.2004
{Neutron star oceans: Instability, mixing, and heat transport}
Urpin
Astron. Astrophys.
421
L5-L8
(2004)
Neutron star oceans: Instability, mixing,.pdf
10.1051/0004-6361:20040165
Stability of the ocean of magnetic neutron stars is considered. We argued that the ocean is unstable if the temperature varies along the surface. The instability grows on a time scale ˜0.1{-}100 s depending on the lengthscale of perturbations and generates a weak turbulence. Turbulence can be responsible for mixing between the surface and deep ocean layers and can enhance heat transport in the surface region.
Urpin.AA.2005
{Instabilities, turbulence, and mixing in the ocean of accreting neutron stars}
Urpin
Astron. \& Astrophys.
438
643-651
(2005)
Instabilities, turbulence, and mixing in the ocean of accreting.pdf
10.1051/0004-6361:20042132
We consider the stability properties of the ocean of accreting magnetic neutron stars. It turns out that the ocean is always unstable due to the combined influence of the temperature and chemical composition gradients along the surface and of the Hall effect. Both the oscillatory and non-oscillatory modes can be unstable in accreting stars. The oscillatory instability grows on a short timescale ~0.1-10 s depending on the lengthscale of a surface inhomogeneity and the wavelength of perturbations. The instability of non-oscillatory modes is typically much slower and can develop on a timescale of hours or days. Instability generates a weak turbulence that can be responsible for mixing between the surface and deep ocean layers and for spreading the accreted material over the stellar surface. Spectral features of heavy elements can be detected in the atmospheres of accreting stars due to mixing, and these features should be different in neutron stars with both stable and unstable burning. Motions caused by instability can also be the reason for slow variations in the luminosity.
Vainshtein.APJ.1992
{Nonlinear restrictions on dynamo action}
{Vainshtein} and {Cattaneo}
apj
393
165--171
(1992)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1992ApJ...393..165V&db_key=AST
10.1086/171494
Vainshtein.GAFD.1983
The macroscopic magnetohydrodynamics of inhomogeneously turbulent cosmic plasmas
Vainshtein and Kichatinov
gafd
24
273-298
(1983)
Vainshtein.ZPMTF.1971
The magnetic field in inhomogeneous turbulent flow
Vainshtein
zpmtf
1
12-18
(1971)
Vedenov.JNEC.1963
Quasi-linear plasma theory (theory of a weakly turbulent plasma)
Vedenov
J. Nucl. Energy. Part C, Plasma Physics
5
169--186
(1963)
Quasi-linear plasma theory (theory of a weakly.pdf
10.1088/0368-3281/5/3/305
The basic principles of the quasi-linear theory of a weakly turbulent plasma are presented. Several processes occurring in a plasma in which collective degrees of freedom are excited are considered: the dynamics of noise build-up in an unstable plasma, the interaction of a beam of charged particles with the plasma, the damping of the plasma waves. The properties of the stationary weakly turbulent state arising in a plasma when a current passes through it are discussed, and so also is the problem of the anomalous diffusion of the plasma across a magnetic field. The phenomenon of `threshold absorption' of large amplitude waves in a plasma, leading to the collisionless heating of the particles, is also examined.
Velikhov.SPJ.1959
Stability of an Ideally Conducting Liquid Flowing Between Cylinders Rotating in a Magnetic Field
Velikhov
Sov. Phys. JETP
36
995--998
(1959)
Weibel.PRL.1959
Spontaneously Growing Transverse Waves in a Plasma Due to an Anisotropic Velocity Distribution
Weibel
Physical Review Letters
2
(1959)
Spontaneously Growing Transverse Waves in a Plasma.pdf
http://link.aps.org/abstract/PRL/v2/p83
Wentzel.APJ.1979
{The dissipation of hydromagnetic surface waves}
{Wentzel}
Astrophys. J.
233
756-764
(1979)
The dissipation of hydromagnetic surface waves.pdf
10.1086/157437
When hydromagnetic surface waves travel along a surface with a thin but finite boundary layer, velocities within this layer become singular when computed according to the ideal MHD equations. The present paper computes the corresponding rate of wave damping. Sufficiently weak surface waves are dissipated either by a resonant conversion into kinetic Alfven waves or by viscosity. Astrophysically important surface waves may involve such large velocity amplitudes outside the narrow zone of linear dissipation that nonlinear phenomena limit the singularity and the method of dissipation. Even these, however, are confined to extremely narrow layers.
Winsor.PF.1968
Geodesic Acoustic Waves in Hydromagnetic Systems
Winsor and Johnson and Dawson
Physics of Fluids
11
2448--2450
(1968)
Geodesic Acoustic Waves in Hydromagnetic Systems.pdf
http://link.aip.org/link/?PFL/11/2448/1
In toroidal systems with geodesic curvature an electrostatic acoustic mode occurs with plasma motion in the magnetic surfaces, perpendicular to the field. In typical stellarators this mode should dominate ordinary sound waves associated with motion along the field.
Wood.JFM.1965
{Properties of inviscid, recirculating flows}
Wood
J. Fluid Mech.
22
337--346
(1965)
Properties of inviscid, recirculating flows.pdf
10.1017/S0022112065000782
Integral relations are derived for steady, incompressible recirculating motions with small viscous forces. The circuit time of a fluid particle on a closed streamline in steady, inviscid flow is shown to be the same for all the closed streamlines on a surface of constant total head.
The discontinuities of velocity and velocity gradient that occur in the motion of inviscid fluid filling a closed, rotating cylinder set in a rotating support with the two rotation axes slightly misaligned are then investigated.
Yang.JHE.2004
{Velocity distribution and dip phenomena in smooth and straight open channel flow}
Yang and Tan and Lim
J. Hydraul. Eng.
130
1179--1186
(2004)
Ying.FED.2004
Exploratory studies of flowing liquid metal divertor options for fusion-relevant magnetic fields in the MTOR facility
Ying and Abdou and Morley and Sketchley and Woolley and Burris and Kaita and Fogarty and Huang and Lao and Narula and Smolentsev and Ulrickson
Fusion Eng. \& Design
72
35--62
(2004)
Exploratory studies of flowing liquid metal.pdf
http://www.sciencedirect.com/science/article/B6V3C-4DBKFGT-1/1/f030e85f48a81dcb8e924645a7d0aeea
This paper reports on experimental findings on liquid metal (LM) free surface flows crossing complex magnetic fields. The experiments involve jet and film flows using GaInSn and are conducted at the UCLA MTOR facility. The goal of this study is to understand the magnetohydrodynamics (MHD) features associated with such a free surface flow in a fusion-relevant magnetic field environment, and determine what LM free surface flow option is most suitable for lithium divertor particle pumping and surface heat removal applications in a near-term experimental plasma device, such as NSTX. Experimental findings indicate that a steady transverse magnetic field, even with gradients typical of NSTX outer divertor conditions, stabilizes a LM jet flow--reducing turbulent disturbances and delaying jet breakup. Important insights into the MHD behavior of liquid metal films under NSTX-like environments are also presented. It is possible to establish an uphill liquid metal film flow on a conducting substrate, although the MHD drag experienced by the flow could be strong and cause the flow to pile-up under simulated NSTX magnetic field conditions. The magnetic field changes the turbulent film flow so that wave structures range from 2D column-type surface disturbances at regions of high magnetic field, to ordinary hydrodynamic turbulence wave structures at regions of low field strength at the outboard. Plans for future work are also presented.
Yusef-Zadeh.APJ.2003
The Origin of the Galactic Center Nonthermal Radio Filaments: Young Stellar Clusters
Yusef-Zadeh
apj
598
325-333
(2003)
Zakharov.EJMB.1999
Statistical theory of gravity and capillary waves on the surface of a finite-depth fluid
Zakharov
European J. Mech. B/Fluids
18
327--344
(1999)
Statistical theory of gravity and capillary waves.pdf
http://www.sciencedirect.com/science/article/B6VKX-3XBTS53-2/2/bb6c7d39ee538a9f003167bab568ffd5
Zakharov.JAMTP.1967
Weak turbulence of capillary waves
Zakharov and Filonenko
J. Appl. Mech. Tech. Phys.
8
37--40
(1967)
Weak turbulence of capillary waves.pdf
http://dx.doi.org/10.1007/BF00915178
In recent years the theory of weak turbulence, i.e. the stochastic theory of nonlinear waves {$[$}I, 9{$]$}, has been intensively developed. In the theory of weak turbulence nonlinearity of waves is assumed to be small; this enables us, using the hypothesis of the random nature of the phases of individual waves, to obtain the kinetic equation for the mean squares of the wave aplitudes.
Zakharov.SPD.1967
{Energy Spectrum for Stochastic Oscillations of the Surface of a Liquid}
{Zakharov} and {Filonenko}
Sov. Phys. Dokl.
11
881
(1967)
Turbulence of Capillary Waves.pdf
Zaqarashvili.AA.2007
Rossby waves in "shallow water" magnetohydrodynamics
Zaqarashvili and Oliver and Ballester and Shergelashvili
Astron. Astrophys.
470
815--820
(2007)
Rossby waves in "shallow water" magnetohydrodynamics.pdf
10.1051/0004-6361:20077382
Zhang.JFM.1995
{On hydromagnetic instabilities driven by the Hartmann boundary layer in a rapidly rotating sphere}
{Zhang} and {Busse}
J. Fluid Mech.
304
263-283
(1995)
On hydromagnetic instabilities driven by the Hartmann boundary.pdf
The instability of an electrically conducting fluid of magnetic diffusivity λ and viscosity v in a rapidly rotating spherical container of magnetic diffusivity $\hat{\lambda}$ in the presence of a toroidal magnetic field is investigated. Attention is focused on the case of a toroidal magnetic field induced by a uniform current density parallel to the axis of rotation, which was first studied by Malkus (1967). We show that the internal ohmic dissipation does not affect the stability of the hydromagnetic solutions obtained by Malkus (1967) in the limit of small λ. It is solely the effect of the magnetic Hartmann boundary layer that causes instabilities of the otherwise stable solutions. When the container is a perfect conductor, $\hat{\lambda}$ = 0, the hydromagnetic instabilities grow at a rate proportional to the magnetic Ekman number of the fluid Eλ; when the container is a nearly perfect insulator, $\lambda/\hat{\lambda}\ll 1$, the hydromagnetic instabilities grow at a rate proportional to E1/2λ; when the container is a nearly perfect conductor, λ 1, the growth rates are proportional to λ, where λ is the magnetic Ekman number based on the diffusivity λ of the container. The main characteristics of the instabilities are not affected by varying magnetic properties of the container. In light of the destabilizing role played by the Hartmann boundary layer, we also examine the corresponding magnetoconvection in a rapidly rotating fluid sphere with the perfectly conducting container and stress-free velocity boundary conditions. Analytical magnetoconvection solutions in closed form are obtained and implications are discussed.
Zhang.PF.1996
Convection in a rotating spherical fluid shell with an inhomogeneous temperature boundary condition at finite Prandtl number
Zhang and Gubbins
pf
8
1141--1148
(1996)
Zhang.PRSLA.1996
{On Small Roberts Number Magnetoconvection in Rapidly Rotating Systems}
Zhang and Jones
Proc. R. Soc. Lond. A
452
981--995
(1996)
On Small Roberts Number Magnetoconvection in Rapidly.pdf
10.1098/rspa.1996.0049
Convection of an electrically conducting fluid of magnetic diffusivity h and thermal diffusivity k in rapidly rotating systems in the presence of an imposed toroidal magnetic field is investigated. The motivation for this study comes from the study of convection in planetary cores. Two important parameters of the system are the Elsasser number L, which measures the strength of the imposed field, and the modified Rayleigh number R, which measures the amplitude of buoyancy forces. In this system both magnetically driven instability due to the field curvature and thermally driven instability due to buoyancy can occur. Attention is focused on the behaviour of linear magnetoconvection at small Roberts number, q = k/h® 0, appropriate for the Earth's core. Two different approaches are adopted for investigation. First, an asymptotic analysis with q ® 0 is carried out to show that R \textc = O(1/q), q ® 0, L ® L \textc, where R \textc is the critical value of the modified Rayleigh number and L \textc denotes the critical value for the purely magnetic instabilities. Moreover, the nature of the transition between magnetically driven modes and thermally driven modes is investigated. Second, numerical solutions at different values of q in a rapidly rotating spherical shell are obtained for two different cases: (i) stress-free boundary conditions with an insulating inner sphere and (ii) no-slip boundary conditions with a conducting inner sphere. Both numerical solutions confirm the singular behaviour of magnetoconvection in the limit q ® 0, as predicted by the asymptotic analysis. In consequence, the transition from the thermally dominant mode to the magnetically dominant mode has a rather complex structure in the limit q ® 0. It is shown that there is no uniform scaling that is appropriate for all O(1) values of L. The results shed new light on well-known numerical difficulties in the problem of magnetoconvection at the small Roberts number limit.
Zhang.SGG.1998
The Dynamical Effects of Hyperviscosity on Numerical Geodynamo Models
Zhang and Jones and Sarson
sgg
42
247--253
(1998)
Zhdanov
Geophysical Inverse Theory and Regularization Problems
Zhdanov
(2002)
Zhou.RMP.2004
Colloquium: Magnetohydrodynamic turbulence and time scales in astrophysical and space plasmas
Zhou and Matthaeus and Dmitruk
rmp
76
1015
(2004)
http://link.aps.org/abstract/RMP/v76/p1015