Lim C.C., Ding X., Nebus J. Vortex Dynamics, Statistical Mechanics, and Planetary Atmospheres

Rensselaer Polytechnic Institute, USA, World Scientifc, London, Singapore, 2009, 222 pp. - ISBN13: 978-981-283-912-1
The focus of this monograph is a physically sound and rigorous, qualitative theory for the end-states or statistically-stationary asymptotic flow states of the forced-damped rotating shallow water equations, with applications to the super-rotation of slowly-rotating terrestrial planets and major moons and the key large-scale features of the Gas Giants in our solar system. Emphasizing the self-organized emergence of these astrophysical atmospheric structures through first and second order phase transitions, the spin-lattice models under Gibbs canonical constraint on the Lagrangian of the underlying dynamics and various microcanonical constraints on total circulations (sums) and enstrophies (square-norms) of relevant physical quantities, are simulated by Monte-Carlo methods, analyzed by mean-field techniques, and rigorously integrated in closed-form where possible by the non-Gaussian non-mean-field spherical model method.Planets and Inspiration.
Barotropic and Shallow-Water Models.
Dynamic Equilibria of the Barotropic Model — Variational Approach.
Statistical Mechanics.
The Monte Carlo Approach.
Phase Transitions in Energy-Relative Enstrophy Models.
Extremal Free Energy in the Mean-Field Theory.
Phase Transitions of Barotropic Flow.
Phase Transitions to Super-Rotation — Exact Closed-Form Solutions.
The Shallow-Water Models — High Energy, Cyclonic Solutions.
The Shallow-Water Model — Low-Energy Solutions.