Tropical cyclone rapid intensification and the excitation of inertia-gravity waves on the edges of an evolving potential vorticity structure

The problem of tropical cyclone rapid intensification is reduced to a potential vorticity (PV) equation and a second order, inhomogeneous, partial differential equation for the azimuthal wind. The latter equation has the form of a Klein-Gordon equation, the right-hand side of which involves the radial derivative of the evolving PV field. When the PV field evolves rapidly, inertia-gravity waves are excited at the edges of the evolving PV structure. In contrast, when the PV field evolves slowly, the second order time derivative term in the Klein-Gordon equation is negligible, inertia-gravity waves are not excited, and the equation reduces to an invertibility principle for the PV. The above concepts are presented in the context of an axisymmetric shallow water model, in both its linear and nonlinear forms. The nonlinear results show a remarkable sensitivity of vortex intensification to the percentage of mass that is diabatically removed from the region inside a given absolute angular momentum surface.