A simple model for nonlinear critical layers in an unstable baroclinic wave.

Abstract

Weakly nonlinear theory is developed for finite-amplitude dynamics of a slightly dissipative baroclinic wave at the point of minimum critical shear in the Beta-plane two-layer model. At this parameter setting the nonlinear theory provides a simple manifestation of critical layer dynamics since the Doppler-shifted frequency vanishes in one of the two layers. Calculations show that when the dissipation is proportional to the potential vorticity and is weak, the new equilibrium steady state has uniform potential vorticity in the critical layer although this is not required for wave stabilization. -from Author