Title:  Super-rotation and Great Red Spots -- statistical mechanics
predictions and simulations 

Chjan Lim, Mathematical Sciences, RPI

Two related problems and a unified approach in the formulation,
analysis and simulation of planetary atmospheres using statistical
mechanics and small LINUX/XP clusters -(1) the super-rotation of the
atmospheres of slowly-rotating planets - namely Venus and Titan and
(2) the formation and stability of large vortex storms on the Gas
Giants such as the Great Red Spot (GRS) on Jupiter and lesser spots on
Uranus, Neptune and Saturn.

Venus' lower atmosphere rotates like a spinning top once every 4 earth
days while the Venusian day is around 243 earth days - this enigma has
defied complete resolution for 6 decades. The Great Red Spot on
Jupiter has been observed for several hundred years and several
explanations have been put forth but none so far predicts correctly
the predominance of anticyclonic vorticity in the formation of these
coherent structures.

Two significant discoveries - (1) on super-rotation we discovered that
at low energies, an idealized planetary atmosphere cannot super-rotate
but may sub-rotate (retrograde motions opposite to the spin of the
planet) provided the planet's spin is large enough. This discovery -
later confirmed in analytical work (see my webpage for papers) -
suggests that slowly-rotating planets can have super-rotating but not
sub-rotating atmospheres. All known slowly-rotating cases in the solar
system - Venus and Titan - have super-rotation.

The second discovery concerns problem (2) on the formation of GRS -
like structures in the Gas Giants and the predominance of anticyclonic
vorticity (anticyclonic means against the planet's rotation assumed
west to east - in the northern hemisphere, this is best represented as
clockwise gyres; a draining bath-tub on the other hand, has cyclonic
or counter-clockwise gyres in the northern hemisphere). Many
scientists have had some success generating GRS-like structures and
demonstrating anticyclonic properties from their numerical models or
lab experiments but an enduring difficulty remains - no completely
satisfactory explanation for anticyclonic predominance have
emerged. In other words, when scientists input the parameter values
for Jupiter's atmosphere into their models, they find end-states which
have GRS and anticyclonic properties - since these models are equally
capable of supporting cyclonic vorticity predominance, they cannot
fully explain the almost universal anticyclonic predominance found in
the Gas Giants.

MC simulations using Jupiter's parameter values finally showed within
the context of the statistical mechanics spin-lattice models that I
introduced, that the anticyclonicity in the GRS-like structures on the
Gas Giants are closely associated with the relatively low mechanical
energy to enstrophy ratios of these self-organizing
phenomena. Enstrophy is the L2 or square-norm of the vorticity field
in the atmosphere. Indeed, since the Venusian super-rotation has a
high energy to enstrophy quotient and the GRS-like structures in the
Gas Giants have low energy to enstrophy quotients, this work covers
the whole range of energy, enstrophy and angular momentum parameter
space.