Chern-Simons approach to atmospheric dynamics

TL;DR

This paper introduces a simplified atmospheric model using a Chern-Simons framework, capturing key physical processes and enabling analytical or perturbative solutions for planetary atmospheres.

Contribution

It presents a novel application of Chern-Simons theory to model planetary atmospheric dynamics with nonlinear differential equations.

Findings

Model includes radiation, diffusion, dissipation effects

Analytic solutions possible in linear case

Perturbative approach for small nonlinearities

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 by its velocity, mass density, temperature and pressure. 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.