Physics – Condensed Matter – Statistical Mechanics
Scientific paper
Feb 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phrva..45.2328m&link_type=abstract
Physical Review A (ISSN 1050-2947), vol. 45, Feb. 15, 1992, p. 2328-2359. Research supported by Shell Foundation.
Physics
Condensed Matter
Statistical Mechanics
113
Equilibrium Flow, Euler Equations Of Motion, Jupiter Red Spot, Statistical Mechanics, Two Dimensional Flow, Conservation Laws, Hamiltonian Functions, Monte Carlo Method, Temperature Distribution, Vorticity
Scientific paper
It is argued that earlier attempts at a comprehensive statistical mechanics for 2D inviscid fluid have been successful mainly due to mistreatment of the infinite family of conserved quantities of Euler flow. The computation that needs to be done is presented in a manner that highlights the role of conserved quantities. Two different methods are given for deriving the mean-field equations that equilibrium configurations of the fluid must satisfy, and the 'dressed-vorticity corollary' is proven. Some illustrative special cases of the mean-field equations are solved, and the Lynden-Bell theory of star clusters is rederived. The connection to the Debye-Hueckel theory of electrolytes and the implications for the Red Spot dynamical simulations of Marcus (1983) are also pointed out.
Cross M. C.
Miller Jonathan
Weichman Peter B.
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