2009: Life Cycles of Hurricane-Like Vorticity Rings

The asymmetric dynamics of potential vorticity mixing in the hurricane inner core are further advanced by examining the end states that result from the unforced evolution of hurricane-like vorticity rings in a non-divergent barotropic model. The results from a sequence of 170 numerical simulations are summarized. The sequence covers a two-dimensional parameter space, with the first parameter defining the hollowness of the vortex (i.e., the ratio of eye to inner-core relative vorticity) and the second parameter defining the thickness of the ring (i.e., the ratio of the inner and outer radii of the ring). In approximately one-half of the cases, the ring becomes barotropically unstable, and there ensues a vigorous vorticity mixing episode between the eye and eyewall. The output of the barotropic model is used to (i) verify that the nonlinear model approximately replicates the linear theory of the fastest-growing azimuthal mode in the early phase of the evolution, and (ii) characterize the end states (defined at t5 48 h) that result from the nonlinear chaotic vorticity advection and mixing. It is found that the linear stability theory is a good guide to the fastest-growing exponential mode in the numerical model. Two additional features are observed in the numerical model results. The first is an azimuthal wavenumber-2 deformation of the vorticity ring that occurs for moderately thick, nearly filled rings. The second is an algebraically growing wavenumber-1 instability (not present in the linear theor