This award provides support for a systematic study of the minimum enstrophy principle and maximum entropy principle as they apply to problems of potential vorticity mixing in hurricanes and larger-scale tropical circulations. Within the context of a barotropic, nondivergent model, theoretical predictions will be extended from the symmetric to the asymmetric case. Of particular interest will be the determination of the bifurcations between the symmetric and asymmetric structures predicted by the maximum entropy vortex arguments. The results of such an asymmetric theory should reveal what kind of steady state asymmetric features are possible in hurricanes. Outside the context of the non-divergent model, both direct numerical integrations and theoretical predictions will be generalized to the shallow water equations (on the plane and on the sphere). This generalization will allow a distinction between vorticity and potential vorticity and a distinction between enstrophy and potential enstrophy, and will allow the energy constraint to include both kinetic and potential energy. The generalization to the quasi-static primitive equations in isentropic coordinates should then follow from the shallow water case. Each step in this investigation will help to improve understanding (and, ultimately, prediction) of the nonlinear evolution of large-scale atmospheric flows.
