The Super- and Sub-Rotation of Barotropic Atmospheres on a Rotating Planet

A statistical mechanics canonical spherical energy-enstrophy theory of the superrotation phenomenon in a quasi-2D barotropic fluid coupled by inviscid topographic torque to a rotating solid body is solved in closed form in Fourier space, with inputs on the value of the energy to enstrophy quotient of the fluid, and two planetary parameters — the radius of the planet and its rate and the axis of spin. This allows calculations that predict the following physical consequences: (A) two critical points associated with the condensation of high and low energy (resp.) states in the form of distinct superrotating and subrotating (resp.) solid-body flows, (B) only solid-body flows having wavenumbers $l=1$, $m=0$ — tiltless rotations — are excited in the ordered phases, (C) the asymmetry between the superrotating and subrotating ordered phases where the subrotation phase transition also requires that the planetary spin is sufficiently large, and thus, less commonly observed than the superrotating phase, (D) nonexcitation of spherical modes with wavenumber $l>1$ in barotropic fluids. Comparisons with other canonical, microcanonical and dynamical theories suggest that this theory complements and completes older theories by predicting the above specific outcomes.