Garner, S. T., N. Nakamura, and I. M. Held, 1992: Nonlinear equilibration
of two-dimensional eady waves: a new perspective. Journal of the
Atmospheric Sciences, 49(21), 1984-1996.
Abstract: The equilibration of two-dimensional baroclinic waves
differs fundamentally from equilibration in three dimensions because two-dimensional
eddies cannot develop meridional temperature or velocity structure. It
was shown in an earlier paper that frontogenesis together with diffusive
mixing in a two-dimensional Eady wave brings positive potential vorticity
(PV) anomalies deep into the atmosphere from both boundaries and allows
the disturbance to settle into a steady state without meridional gradients.
Here we depart from the earlier explanation of this equilibration and associate
the PVintrusions with essentially the same kind of vortex "roll-up"
that characterizes the evolution of barotropic shear layers. To avoid subgrid
turbulence parameterizations and computational diffusion, the analogy is
developed using Eady's generalized baroclinic instability problem. Eady's
generalized model has two semi-infinite regions of large PV surrounding
a layer of relatively small PV. Without boundaries, frontal collapse, or
strong diffusion the model still produces equilibrated states, with structure
similar to the vortex streets that emerge from unstable barotropic shear
layers. The similarity is greatest when the baroclinic development is viewed
in isentropic coordinates. The contrast between the present equilibrated
solutions, which exhibit no vertical tilt, and Blumen's diffusive frontogenesis
model, which allows the wave to retain its phase tilt, is briefly discussed.
The equilibration of two-dimensional baroclinic waves differs fundamentally
from equilibration in three dimensions because two-dimensional eddies cannot
develop meridional temperature or velocity structure. It was shown in an
earlier paper that frontogenesis together with diffusive mixing in a two-dimensional
Eady wave brings positive potential vorticity (PV) anomalies deep into
the atmosphere from both boundaries and allows the disturbance to settle
into a steady state without meridional gradients. Here we depart from the
earlier explanation of this equilibration and associate the PVintrusions
with essentially the same kind of vortex "roll-up" that characterizes
the evolution of barotropic shear layers. To avoid subgrid turbulence parameterizations
and computational diffusion, the analogy is developed using Eady's generalized
baroclinic instability problem. Eady's generalized model has two semi-infinite
regions of large PV surrounding a layer of relatively small PV. Without
boundaries, frontal collapse, or strong diffusion the model still produces
equilibrated states, with structure similar to the vortex streets that
emerge from unstable barotropic shear layers. The similarity is greatest
when the baroclinic development is viewed in isentropic coordinates. The
contrast between the present equilibrated solutions, which exhibit no vertical
tilt, and Blumen's diffusive frontogenesis model, which allows the wave
to retain its phase tilt, is briefly discussed.