A Forced, Balanced Model for Tropical Cyclone Intensification

To understand the time evolution of the tropical cyclone, a simplified, axisymmetric, one-layer, analytic model of tropical cyclone intensification is developed using the wave-vortex approximation, an assumption to the kinetic energy. In filtering the inertia-gravity waves, the problem is reduced to the prediction of the potential vorticity and the inversion of the potential vorticity to obtain balanced wind and mass fields. We evaluate the evolution of the tangential wind and total energy through a series of experiments in which we change the radial distributions of a mass sink forcing. Through these experiments, we gain insight into why tropical cyclones have long incubation times before rapid intensification and into how hollow potential vorticity structures develop in the inviscid flow above the boundary layer. We also compare this model to a model that uses the gradient balance relation. We find that the model based on the wave-vortex approximation is best suited to fluids with flow speeds indicative of the external vertical normal mode in which case the change in fluid depth is small.