A Model of Two Dimensional Turbulence Using Random Matrix Theory

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 regularizat...

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Bibliographic Details
Published in:arXiv.org 2002-06
Main Authors: Iyer, Savitri V, Rajeev, S G
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Entropy
Fluid flow
Incompressible flow
Inviscid flow
Matrix theory
Maximum entropy
Regularization
Two dimensional flow
Two dimensional models
Vorticity
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0206083