2016 Volume 94 Issue 2 Pages 119-135
A simplified, axisymmetric, one-layer model of tropical cyclone intensification is presented. The model is based on the Salmon wave-vortex approximation, which can describe flows with low Froude number and arbitrary Rossby number. After introducing an additional approximation designed to filter propagating inertia-gravity waves, the problem is reduced to the prediction of potential vorticity (PV) and the inversion of this PV to obtain the balanced wind and mass fields. This PV prediction/inversion problem is solved analytically for two types of forcing: a two-region model in which there is nonzero forcing in the cyclone core and zero forcing in the far-field and a three-region model in which there is nonzero forcing in both the cyclone core and the eyewall, with zero forcing in the far-field. The solutions of the two-region model provide insight into why tropical cyclones can have long incubation times before rapid intensification and how the size of the mature vortex can be influenced by the size of the initial vortex. The solutions of the three-region model provide insight into the formation of hollow PV structures and the inward movement of angular momentum surfaces across the radius of maximum wind.