THE DEVELOPMENT OF POTENTIAL VORTICITY IN A HURRICANE-LIKE VORTEX

We investigate the time evolution of the potential-vorticity distribut ion in an axisymmetric hurricane-like vortex using a numerical model b ased on a formulation by Schubert and Alworth. In particular, we compa re the vortex response to an annular heating function with that in the analytic calculation by Schubert and Alworth in which the maximum hea ting rate occurs on the vortex axis. The annular heating function is i ntended to better represent the latent-heat release in the eye-wall cl ouds of a hurricane. We show that after about four days of integration time in the Schubert-Alworth calculation, the isentropes near the vor tex centre, and hence the prescribed heating function, become concentr ated near the surface in physical space. In comparison, for the annula r heating distribution the descent of the isentropes is less marked an d the vertical distribution of the heating in physical space remains m ore realistic vis-a-vis a hurricane. It is significant that in this ca se the potential-vorticity maximum lies not on the vortex axis, as in the Schubert-Alworth calculation, but close to the radius of maximum h eating. This appears to be consistent with observations in hurricanes. Finally we show that, counter to intuition, there is greater subsiden ce on the vortex axis in the case where the heating is a maximum on th e axis. A dynamical explanation is offered for this result.