After an eye forms in a hurricane, the convective heating pattern has the shape of an annulus or doughnut, with no convective heating in the center. The annular ring of convection makes the potential vorticity (and also the vorticity) high in an annular ring. In three dimensions the resulting spatial structure of the PV field might then be expected to be a tower of high PV with a hole in the center or, equivalently, a hollow tower of PV. The reversal of the radial gradient of PV in such a flow field might also be expected to set the stage for dynamic instability and rearrangement of the PV distribution. If, during the rearrangement process, part of the low PV fluid in the eye is mixed into the eyewall, asymmetric eye contraction can occur in conjunction with a polygonal eyewall. Hollow PV structures are associated with ``U-shaped" radial profiles of the tangential wind. If the vorticity redistribution is violent enough, an end state with the highest vorticity in the center is reached. After this rearrangement of vorticity, the tangential wind field is no longer ``U-shaped." This process can be simulated with a variety of numerical models of different complexity. Interestingly, the end state can also be predicted analytically using concepts of selective decay from 2-D turbulence theory. This involves the calculus of variations solution to the problem of minimizing enstrophy under the constraints of fixed angular momentum and fixed energy.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics