A NUMERICAL MODEL OF THE SLOWLY VARYING TROPICAL CYCLONE IN ISENTROPIC COORDINATES

Abstract

A diagnostic axisymmetric model in isentropic coordinates is developed to study the effect of differential heating on the dynamics and energetics of the steady-state tropical cyclone. From the thermal forcing specified by various heating distributions, slowly varying solutions for the mass and momentum fields are obtained by an iterative technique. The theory of available potential energy for open systems is utilized to study the energy budget for the hurricane. In the slowly varying state, the gain of available potential energy by diabatic heating and lateral boundary processes balances the conversion of potential to kinetic energy that, in turn, offsets frictional dissipation. For a domain of radius 500 km, the boundary flux of available potential energy is about 40 percent of the generation by diabatic heating. For a domain of radius 1000 km, however, the boundary flux is about 15 percent of the generation. Horizontal and vertical mixing are studied through the use of constant exchange coefficients. As the horizontal mixing decreases, the maximum surface wind increases and moves closer to the center. Several horizontal and two vertical distributions of latent heating are investigated. The maximum surface wind is dependent primarily on heating within 100 km. The transverse (radial) circulation is closely related to the heat release beyond 100 km. In experiments in which the vertical variation of heating is pseudoadiabatic, the temperature and outflow structures are unrealistic. A vertical distribution that releases a higher proportion of heat in the upper troposphere yields results that are more representative of the hurricane.