Nonlinear geostrophic adjustment, cyclone/anticyclone asymmetry, and potential vorticity rearrangement

Abstract

Within the context of the rotating shallow water equations, it is shown how initially unbalanced states possessing certain symmetries dynamically evolve to lose those symmetries during nonlinear geostrophic adjustment. Using conservation law methods, it is demonstrated that the adjustment of equal and opposite (circular) mass imbalances results in a balanced end state where cyclones are stronger than anticyclones; the reverse holds true for momentum imbalances. In both cases, the degree of this asymmetry is shown to be directly proportional to the amount of initial imbalance (a measure of the nonlinearity occurring during time-dependent adjustment). On the other hand, the degree of asymmetry is maximal for imbalances of Rossby deformation scale. As for the potential vorticity, it is shown that its final profile can be noticeably different from its initial one; from an Eulerian perspective, this rearrangement is not confined to uniform shifts of potential vorticity fronts. Direct 2D numerical initial value problems confirm the asymmetry in the predicted final states and establish a relatively fast time scale for adjustment to complete. The robustness of these results is confirmed by studying, in addition, the adjustment of elliptical mass imbalances. The numerical integrations reveal that, during geostrophic adjustment, potential vorticity rearrangement occurs irreversibly on a fast wave time scale.