An Analytical Theory of Tropical Cyclone Motion Using a Barotropic Model

Roger K. Smith Meteorologisches Institut, Universität München, München, Federal Republic of Germany

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Wolfgang Ulrich Meteorologisches Institut, Universität München, München, Federal Republic of Germany

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Abstract

An analytical theory is presented for the motion of an initially symmetric barotropic vortex on a beta-plane at rest, the prototype problem in the theory of tropical cyclone motion. In the case of vortices with parameter values appropriate to tropical cyclones, the theory shows excellent agreement with equivalent numerical model calculations for a period of between one and two days. In particular, the vortex track and the evolution of vortex asymmetries, the so-called beta gyres, are accurately predicted. The calculations provide further insight into dynamics of tropical cyclone motion in general and provide a firmer basis for interpreting the numerical solutions in particular. They are relevant also to the important problem of designing more appropriate “bogus” vortices for the initialization of dynamically based tropical cyclone forecast models.

Abstract

An analytical theory is presented for the motion of an initially symmetric barotropic vortex on a beta-plane at rest, the prototype problem in the theory of tropical cyclone motion. In the case of vortices with parameter values appropriate to tropical cyclones, the theory shows excellent agreement with equivalent numerical model calculations for a period of between one and two days. In particular, the vortex track and the evolution of vortex asymmetries, the so-called beta gyres, are accurately predicted. The calculations provide further insight into dynamics of tropical cyclone motion in general and provide a firmer basis for interpreting the numerical solutions in particular. They are relevant also to the important problem of designing more appropriate “bogus” vortices for the initialization of dynamically based tropical cyclone forecast models.

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