Two Dynamic Regimes of Finite Amplitude Charney and Green Waves

Abstract

The weakly nonlinear evolutions of the Green and Charney waves are compared for two regimes: (1) when internal dissipation is the dominant dissipation; (2) when Ekman friction is the dominant dissipation. When the Ekman dissipation is dominant, we obtain a large amplitude equilibrated wave state which depends upon the initial conditions but not upon the magnitudes of the dissipation; the steady wave features a barotropic structure, and does not transport heat in the meridional direction. In sharp contrast, when internal dissipation is dominant, a small amplitude, equilibrated wave state is found, which is independent of the initial conditions but depends on the magnitude of the internal dissipation. The steady wave exhibits a westward phase tilt and transports heat poleward by an amount proportional to the internal dissipation. The presence of a large planetary vorticity gradient stabilizes the finite amplitude evolution of the planetary waves and leads to a stable equilibrium planetary wave state.