A Model of Two Dimensional Turbulence Using Random Matrix Theory
摘要
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.
引用
@article{arxiv.physics/0206083,
title = {A Model of Two Dimensional Turbulence Using Random Matrix Theory},
author = {Savitri V. Iyer and S. G. Rajeev},
journal= {arXiv preprint arXiv:physics/0206083},
year = {2009}
}
备注
latex, 12 pages, 2 figures, acknowledgement added