Forced Baroclinic Wave Dynamics at Minimum Critical Shear: Potential Vorticity Homogenization, Vacillation, and Equilibration

Abstract

Finite-amplitude dynamics of a slightly dissipative baroclinic wave in a two-layer, ?-plane channel model at the point of minimum critical shear are examined. At this point, both the potential vorticity gradient and the Doppler-shifted frequency vanish within the lower layer. Previous studies have shown that for this parameter setting both the magnitude of the dissipation and the harmonics of the fundamental wave play important roles in the nonlinear dynamics of the system. In the present study, the response of the nonlinear dynamical system to zonally varying potential vorticity forcing is examined. When the forcing and dissipation are asymptotically small and of equal magnitude, an analytical analysis indicates that the fundamental wave equilibrates to a steady amplitude regardless of the mode being forced. For sufficiently strong forcing, the system must be solved numerically, in which case it is shown that when a harmonic of the fundamental is forced, the system can exhibit one of two dynamical regimes: steady state or vacillatory. The latter can only exist in the presence of forcing. In sharp contrast, directly forcing the fundamental always results in equilibration of the system. In cases where the fundamental wave equilibrates, it is shown that the total potential vorticity (basic state plus disturbance) may homogenize along streamlines of the fundamental wave, leading to strong vortex formation.