Chjan Lim
110, 8th Street, NY 121803590, Troy, NY, USA
Rensselaer Polytechnic Institute, Troy, NY
Publications:
Lim C. C.
The Super and SubRotation of Barotropic Atmospheres on a Rotating Planet
2022, Vol. 18, no. 1, pp. 1942
Abstract
A statistical mechanics canonical spherical energyenstrophy theory of the superrotation phenomenon in a quasi2D 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.) solidbody flows, (B) only solidbody 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.

Lim C. C.
Phase Transition to Quadrupolar Vortices in a Spherical Model of the EnergyEnstrophy Theory — Exact Solution
2020, Vol. 16, no. 4, pp. 543555
Abstract
A new energyenstrophy model for the equilibrium statistical mechanics of barotropic flow
on a sphere is introduced and solved exactly for phase transitions to quadrupolar vortices when
the kinetic energy level is high. Unlike the Kraichnan theory, which is a Gaussian model, we
substitute a microcanonical enstrophy constraint for the usual canonical one, a step which is based
on sound physical principles. This yields a spherical model with zero total circulation, a microcanonical
enstrophy constraint and a canonical constraint on energy, with angular momentum fixed
to zero. A closedform solution of this spherical model, obtained by the Kac – Berlin method
of steepest descent, provides critical temperatures and amplitudes of the symmetrybreaking
quadrupolar vortices. This model and its results differ from previous solvable models for related
phenomena in the sense that they are not based on a meanfield assumption.
