Chern-Simons approach to atmospheric dynamics

Abstract

A simplified model for a planet's atmosphere as an open two-dimensional Chern-Simons system is presented. The dynamical variables describe an ideal gas with velocity v, density ρ, temperature T and pressure P . Radiation exchange, diffusion and mechanical dissipation are also included. The resulting dynamics is given by a set of nonlinear differential equations of first order in time for the densities of energy, momentum and mass. The initial value problem can be integrated given the radiation balance of the planet. If the nonlinearities could be neglected the integration can be done in analytic form and small nonlinearities can be incorporated as perturbative corrections.