Relationships between the main parameters of the stationary two-dimensional vortical flows in the planetary atmosphere

Abstract

In a two-dimensional (2D) model of the planetary atmosphere, the convective flow of vorticity represents a strong non-linearity able to drive the fluid toward a quasi-coherent vortical pattern. This is similar to the highly organized 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. Restricting to a purely hydrodynamic model we have derived a differential equation governing the stationary, 2D, highly organized vortical flows in the planetary atmosphere. After briefly recalling the derivation, 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 with observational data are favorable and several relationships were 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.

Keywords:

• Atmospheric vortex
• Action functional
• Field theory
• Self-duality
• Tropical cyclone

Acknowledgement

This work has been partly supported by the Romanian Ministry of Education and Research.