Schedule Jun 3
Exact solution of a three constraints equilibrium statistical mechanics model for 2-D turbulence
C. Lim (RPI)
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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