dorsal/arxiv
View SchemaA Model of Two Dimensional Turbulence Using Random Matrix Theory
| Authors | Savitri V. Iyer, S. G. Rajeev |
|---|---|
| Categories | |
| ArXiv ID | physics/0206083 |
| URL | https://arxiv.org/abs/physics/0206083 |
| DOI | 10.1142/S0217732302007934 |
| Journal | Mod.Phys.Lett. A17 (2002) 1539-1550 |
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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"abstract": "We derive a formula for the entropy of two dimensional incompressible\ninviscid flow, by determining the volume of the space of vorticity\ndistributions with fixed values for the moments Q_k= \\int_w(x)^k d^2 x. This\nspace is approximated by a sequence of spaces of finite volume, by using a\nregularization of the system that is geometrically natural and connected with\nthe theory of random matrices. In taking the limit we get a simple formula for\nthe entropy of a vortex field. We predict vorticity distributions of maximum\nentropy with given mean vorticity and enstrophy; also we predict the\ncylindrically symmetric vortex field with maximum entropy. This could be an\napproximate description of a hurricane.",
"arxiv_id": "physics/0206083",
"authors": [
"Savitri V. Iyer",
"S. G. Rajeev"
],
"categories": [
"physics.flu-dyn",
"hep-th"
],
"doi": "10.1142/S0217732302007934",
"journal_ref": "Mod.Phys.Lett. A17 (2002) 1539-1550",
"title": "A Model of Two Dimensional Turbulence Using Random Matrix Theory",
"url": "https://arxiv.org/abs/physics/0206083"
},
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