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

The kinetic energy of barotropic flow coupled to an infinitely 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 2D Ising model of ferromagnetism, is used to find the barotropic vorticity states at thermal equilibrium for a 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.