Analytical Predictions for Zonally Symmetric Equilibrium States of the Stratospheric Polar Vortex

Abstract

Equilibrium states of initially barotropically unstable polar vortices are predicted using two different approaches: minimum enstrophy and maximum entropy theories, which have been extended to include flows evolving on the surface of a sphere. Minimum enstrophy theory shows very good agreement with an ensemble of direct numerical integrations of a polar vortex that mixes vorticity mainly on a spherical cap. For the case of a polar vortex with a substantial resistance to vorticity mixing at its core, the maximum entropy prediction shows good consistency with an ensemble of direct numerical integrations. Maximum entropy theory gives an additional source of information with its density functions, which in a probabilistic sense reveal how the vorticity field (and therefore the mass field) is redistributed in the equilibrium state. The density functions show good skill in predicting several passive tracer distributions in the numerical experiments. Also, from a local point of view, density functions determine the degree of mixing of initially well separated air masses, information that is valuable in tracing atmospheric chemical components.