The Roles of Barotropic Instability and Beta Effect in Eyewall Evolution of Tropical Cyclones

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 exponentially growing PV waves. In this study, such instability and the subsequent nonlinear evolutions of three TC-like vortices with different degrees of hollowness PV ring 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 interaction 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 inner-core circulation, it is shown in this study 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 greater beta parameter tends to experience an earlier breakdown along with the enhanced radial gradients of the basic-state (azimuthal mean) angular velocity, followed by wave-wave and wave-flow interactions, leading to earlier merger and axisymmetrization processes. This 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.