Phase transitions of barotropic flow coupled to a massive rotating sphere - derivation of a fixed point equation by the Bragg method

TL;DR

This paper models the kinetic energy of barotropic flow on a rotating sphere using a spin-lattice approach, deriving a fixed point equation for equilibrium states through a mean field approximation inspired by the Ising model.

Contribution

It introduces a novel spin-lattice model for barotropic flow on a sphere and derives a fixed point equation for equilibrium states using a mean field approximation.

Findings

Derivation of a fixed point equation for flow states

Application of a spin-lattice model to planetary atmospheres

Identification of equilibrium vorticity states

Abstract

The kinetic energy of barotropic flow coupled to an infnitely massive rotating sphere by an unresolved complex torque mechanism is approximated by a discrete spin-lattice model of fluid vorticity on a rotating sphere, analogous to a one-step renormalized Ising model on a sphere with global interactions. The constrained energy functional is a function of spin-spin coupling and spin coupling with the rotation of the sphere. A mean field approximation similar to the Curie-Weiss theory, modeled after that used by Bragg and Williams to treat a two dimensional Ising model of ferromagnetism, is used to find the barotropic vorticity states at thermal equilibrium for given temperature and rotational frequency of the sphere. A fixed point equation for the most probable barotropic flow state is one of the main results.