In a hurricane, the concentrated potential vorticity (PV) source due to heating in the eyewall can result in a reversal of the radial PV gradient, allowing the vortex to become barotropically unstable. In this manner an axisymmetric vortex can develop asymmetries, redistribute PV through chaotic nonlinear mixing, and eventually resymmetrize with a different, stable structure. Recent studies of this process have provided insight into diverse aspects of hurricane dynamics, including the development of spiral bands and mesoscale vortices, the existence of polygonal eyewalls, and asymmetric eye contraction.

While PV is conserved following the motion, nonlinear redistribution of PV results in filamentation which cannot be followed accurately by deterministic models with limited resolution. Consequently, various statistical approaches (such as minimum enstrophy and maximum entropy) have been proposed to compute equilibrium solutions. Most studies of this process to date have applied these methods in the simplest dynamical context, namely, two-dimensional nondivergent incompressible flow. This paper will concentrate on the extension of these ideas to the next level of dynamical complexity, namely, the shallow-water equations. We will review the analytical formulation of the maximum entropy method, describe an iterative method for its solution, and present results and discuss their implications for hurricane dynamics.