Mesoscale Barotropic Instability of Vortex Rossby Waves in Tropical Cyclones

In this study, the barotropic stability of vortex Rossby waves (VRWs) in 2D inviscid tropical cyclone (TC)-like vortices is explored in the context of rotational dynamics on an f-plane. Two necessary instable conditions are discovered: (a) there must be at least one zero point of basic vorticity gradient in the radial scope; and (b) the relative propagation velocity of perturbations must be negative to the basic vorticity gradient, which reflects the restriction relationship of instable energy. The maximum growth rate of instable waves depends on the peak radial gradient of the mean vorticity and the tangential wavenumber (WN). The vortex-semicircle theorem is also derived to provide bounds on the growth rates and phase speeds of VRWs. The typical basic states and different WN perturbations in a tropical cyclone (TC) are obtained from a high resolution simulation. It is shown that the first necessary condition for vortex barotropic instability can be easily met at the radius of maximum vorticity (RMV). The wave energy tends to decay (grow) inside (outside) the RMV due mainly to the negative (positive) sign of the radial gradient of the mean absolute vorticity. This finding appears to help explain the developemnt of strong vortices in the eyewall of TCs.