Experiments with a Spectral Tropical Cyclone Model

Abstract

Abstract The three-layer balanced axisymmetric tropical cyclone model presented by Ooyama is generalized to dimensions and the resultant primitive equations are solved using the spectral (Galerkin) method with Fourier basis functions on a doubly-periodic midlatitude β-plane. The nonlinear terms are evaluated using the transform method where the necessary transforms are performed using FFT algorithms. The spectral equations are transformed so that the dependent variables represent the normal modes of the linearized equations. For the three-layer model, the normal modes correspond to internal or external gravity or rotational modes or to inertial oscillations associated with the constant depth boundary layer. When the governing equations, are written in terms of the normal modes, the linear terms can be evaluated exactly and the application of the nonlinear normal mode initialization scheme proposed by Machenhauer is straightforward. Results from a simulation with an axisymmetric initial condition on an f-p...