Phase transitions to Super-rotation in a Coupled Fluid - Rotating Sphere System

A family of spin-lattice models are derived as convergent finite dimensional approximations to the rest frame kinetic energy of a barotropic fluid coupled to a massive rotating sphere. The angular momentum of the fluid component changes under complex torques that are not resolved and the kinetic energy of the fluid is not a conserved Hamiltonian in these models. These models are used in a statistical equilibrium formulation for the energy relative enstrophy theory of the coupled barotropic fluid rotating sphere system, known as Kac’s spherical model, to study the interactions between the energy cascade to large scales and angular momentum transfer. Exact solution of this model provides critical temperatures and amplitudes of the ground modes super-rotating solid body flows in the BECondensed phase.