Motivated by observations of cyclone/anticyclone asymmetry in the shallow water equations, we show how unbalanced states initially possessing certain symmetries dynamically evolve to lose those symmetries during geostrophic adjustment. Studying both rectilinear and axisymmetric flow configurations, it is shown that the degree of asymmetry in the final state is always 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 reaches a local maximum for flows that are initially on the scale of the deformation radius. 2-D numerical initial value problems explicitly show the time development of asymmetry and verify the robustness of the asymmetry in the predicted final states. Finally, it is shown that when nonlinear effects are important, the potential vorticity of the flow in the final state can be quite different from its initial configuration, a feature which is absent from linear geostrophic adjustment. We conjecture that gravity wave coupling to the vortical component of the flow is essential to producing such a change, thus making geostrophic adjustment a mechanism for irreversible potential vorticity rearrangement.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics