Potential vorticity rings and eye subsidence

The intense diabatic heating in hurricane eyewalls produces an annular ring of high potential vorticity (PV). If narrow enough, such PV rings can be very unstable. We have studied the instability and nonlinear evolution of such PV rings in the context of nondivergent barotropic dynamics and divergent barotropic (i.e., shallow water) dynamics. Systematic sets of experiments have been performed for unforced and forced PV rings. Several types of evolution have been found, including relaxation to a PV monopole, mesovortex formation, and chaotic patterns of mesovortices. The experiments that produce mesovortices raise interesting questions about the ability of hurricanes to radiate intertia-gravity waves. During PV mixing the radial distribution of inertial stability can be substantially modified, which can cause changes in the transverse circulation. We have studied such effects by deriving simplified solutions of the Eliassen transverse circulation equation.