| Abstract: | Diabatic heating by convection in the eyewall often produces an annular region of high potential vorticity (PV) around the relatively low PV eye in a strong tropical cyclone (TC). Such a PV ring is barotropically unstable and can encourage the exponential growth of PV waves. In this study, such instability and the subsequent nonlinear evolution of three TC-like vortices having PV rings with different degrees of hollowness on an f-plane are first examined using an unforced, inviscid shallow-water-equation model. Results show that the simulated eyewalls evolve similarly to those in the nondivergent barotropic model. It is also found that the polygonal eyewall structure can be decomposed into vortex Rossby waves (VRWs) of different wavenumbers with different amplitudes, allowing for wave-wave interactions to produce complicated behaviors of mesovortices in the TC eyewall. The same set of PV rings has been examined on a beta-plane. Although the beta effect has been rendered unimportant to the eyewall evolution due to the relatively small scale of the inner-core circulation, this study shows that the beta effect may erode the coherent structure of mesovortices in the eyewall of an initially hollow PV-ring vortex. Mesovortices modeled on the beta-plane with a greater beta parameter tend to experience an earlier breakdown and enhanced radial gradients of the basic-state (azimuthally mean) angular velocity, followed by wave-wave, wave-flow interactions, leading to earlier merger and axisymmetrization processes. This result implies that the beta effect could be one of the forcings that shorten the lifetime of quasi-steady mesovortices in the eyewall of real TCs. |
