Vacillations in a Shallow-Water Model of the Stratosphere

Abstract

The evolution of the polar vortex in a shallow-water model with time-independent topographic forcing and relaxation to a constant equilibrium state is investigated for a range of topographic forcing amplitudes. For small forcing amplitudes there are only weak disturbances on the edge of the polar vortex and the vortex area remains constant, whereas for large amplitudes there are cycles where the vortex breaks down and then reforms (and zonal winds vacillate between westerlies and easterlies). Analysis of the mass within potential vorticity (PV) contours shows that these vacillations are due to out-of-phase variations in the mass fluxes across PV contours due to the relaxation and to hyperdiffusion. During the strong vortex stages Rossby wave breaking produces a cascade of PV to small scales, and these small-scale features are eventually eliminated by hyperdiffusion. This causes a decrease in the mass within the high PV contours and ultimately the destruction of the vortex. In contrast, during stages with no vortex there are very weak PV gradients, weak Rossby wave activity, and little cascade of PV to small scales. The vortex, and PV gradients, are then reestablished by the mass fluxes due to the diabatic relaxation term. These results suggest that the horizontal PV structure may play an important role in the vortex breakdown and recovery in three-dimensional models and in the real stratosphere.