Scaling laws for the tropical cyclone derived from the stationary atmospheric vortex equation

Abstract

In a two-dimensional model of the planetary atmosphere the compressible convective flow of vorticity represents a strong nonlinearity able to drive the fluid toward a quasi-coherent vortical pattern. This is similar to the highly organised motion generated at relaxation in ideal Euler fluids. The problem of the atmosphere is however fundamentally different since now there is an intrinsic length, the Rossby radius. Within the Charney Hasegawa Mima model it has been derived a differential equation governing the stationary, two-dimensional, highly organised vortical flows in the planetary atmosphere. We present results of a numerical study of this differential equation. The most characteristic solution shows a strong similarity with the morphology of a tropical cyclone. Quantitative comparisons are also favorable and several relationships can be derived connecting the characteristic physical parameters of the tropical cyclone: the radius of the eye-wall, the maximum azimuthal velocity and the radial extension of the vortex.