Jun 3
Exact solution of a three constraints equilibrium statistical mechanics model for 2-D turbulence
C. Lim (RPI)
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This three constraints model is the third one in a family of few constraints
equilibrium statistical mechanics models proposed by Turkington and Majda
for the study of 2-D and quasi-geostrophic flows. This model is equivalent
to the Batchelor-Lee-Kraichnan model for inverse cascades after a
Fourier transform. The exact solution of this model is based on a simple but
fundamental observation that the enstrophy corresponds exactly to the higher dimen
sional spherical constraint introduced by Kac. The exact solution is
then obtained by extending Kac's and Berlin's solution of the spherical
model to a long range logarithmic interaction. A negative critical
temperature for phase transition to coherent structures is obtained.
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