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A Model of Two Dimensional Turbulence Using Random Matrix Theory

Savitri V. Iyer·S. G. Rajeev
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Abstract

We derive a formula for the entropy of two dimensional incompressible inviscid flow, by determining the volume of the space of vorticity distributions with fixed values for the moments Q_k= \int_w(x)^k d^2 x. This space is approximated by a sequence of spaces of finite volume, by using a regularization of the system that is geometrically natural and connected with the theory of random matrices. In taking the limit we get a simple formula for the entropy of a vortex field. We predict vorticity distributions of maximum entropy with given mean vorticity and enstrophy; also we predict the cylindrically symmetric vortex field with maximum entropy. This could be an approximate description of a hurricane.

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Savitri V. Iyer, S. G. Rajeev. 2002-06-26. A Model of Two Dimensional Turbulence Using Random Matrix Theory. https://doi.org/10.1142/s0217732302007934

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