The Generation and Maintenance of Hollow PV Towers in a Forced Primitive Equation Model

Diabatic heating from deep moist convection in the hurricane eyewall produces a towering annular structure of elevated potential vorticity (PV), known as a hollow PV tower. The sign reversal of the radial gradient of PV satisfies the Charney-Stern necessary condition for combined barotropic-baroclinic instability. For sufficiently thin annular structures, small perturbations grow exponentially, extract energy from the mean flow, and lead to hollow tower breakdown, with significant vortex structural and intensity change. A forced primitive equation model in isentropic coordinates is used to understand the role of diabatic and frictional effects in the generation, maintenance, and breakdown of the hurricane PV tower. Diabatic heating is parameterized as an annular heating ring of variable width, depth, and magnitude, and the nonlinear evolution of tropical storm–like vortices is examined under this forcing. Diabatic heating produces a strengthening and thinning PV tower in time due to the combined effects of the diabatic heating and radial PV advection by the induced secondary circulation. If the forcing makes the eyewall thin enough, then it can become dynamically unstable and cause air parcels with high PV to be mixed preferentially into the eye at lower levels, where unstable PV wave growth rates are largest. The breakdown of the hollow PV tower leads to a transient break in vortex intensification, a decrease in minimum central pressure, an inward shift of absolute angular momentum surfaces at low levels, and the development of warm anomalies within the center of the vortex. Horizontal and vertical diffusion are shown to help stabilize and maintain the PV tower by reducing the eyewall PV and the unstable-mode barotropic growth rate. Finally, it is shown that the heating-induced secondary circulation helps to maintain the PV tower structure.