A field theoretical model of stationary atmospheric vortices

A local two dimensional approximation of the planetary atmosphere allows the representation of the vorticity dynamics in terms of a collection of point-like vortices interacting in plane by a potential. This can be formalized in the continuum limit as a field theory where the matter (density of vortices) is represented by a complex function and the interacting potential by a gauge field with Chern-Simons action. We construct the Lagrangian density, first in the ideal Eulerian case, where the potential is long-range, Coulombian. The extremum of the action leads to the sinh-Poisson equation at stationarity, confirming a result known from numerical simulation. For the planetary atmosphere the interaction range is finite, given by the Rossby radius. The equation of quasi-stationary states is derived. 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.