A Model of Two Dimensional Turbulence Using Random Matrix Theory

Details A Model of Two Dimensional Turbulence Using Random Matrix Theory A Model of Two Dimensional Turbulence Using Random Matrix Theory

2002-06-25

arxiv.org/abs/physics/0206083v2

Mod.Phys.Lett. A17 (2002) 1539-1550

Physics

Fluid Dynamics

latex, 12 pages, 2 figures, acknowledgement added

Scientific paper

10.1142/S0217732302007934

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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