Analytical Solutions of Vortex Rossby Waves Associated with Vortex Resiliency of Tropical Cyclones

We analytically solve a forced linear problem of vortex Rossby waves (VRWs) associated with the vortex resiliency of tropical cyclones. We consider VRWs on a basic barotropic axisymmetric vortex. VRWs, which are initially absent, are successively forced by a vertically sheared unidirectional environmental flow. The problem is formulated in the quasigeostrophic equations, linearized about the basic vortex. The basic potential vorticity (PV) is assumed to be piecewise constant in the radial direction so that the problem can be analytically solved. The obtained solutions show the following.