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Abstract: This paper gives a microscopic derivation of the equilibrium energy density spectrum (per unit flow area) for the 2D Euler equations in a unbounded domain. The spectral density per unit flow area in the fundamental wavenumber interval q to q + 1 is given by E (q) = 16 3 K " dJ 1 (q + e(q)) q 2 # where scale factor 0 < d ! 1; and phase shift 0 < e(q) ! 0 as q !1: This derivation is based on a connection between the point vortex gas and the statistics of random matrices due to Wigner and Ginibre. ... (Update)
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BibTeX entry: (Update)
@misc{ lim-equilibrium,
author = "Chjan C. Lim",
title = "Equilibrium Energy Density Spectrum for Two Dimensional Ows in the Zero
Viscosity Limit and Random Matrices",
url = "citeseer.ist.psu.edu/484003.html" }
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2 ects of the forcing function spectrum on the energy spectrum.. (context) - Constantin, Foias et al. - 1994
1 A microscopic derivation of the equilibrium energy spectrum .. (context) - Lim - 2001
1 and applications to universality questions in random matrix .. (context) - Deift, McLaughlin et al. - 1999
1 A long range spherical model and exact non-Gaussian solution.. - Lim - 2001
1 Energy spectrum in the inertial and dissipation ranges of 2-.. (context) - Gotoh - 1998
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1 The kinetic energy spectrum of the 2-D enstrophy turbulence .. (context) - Lindborg, Alvelius - 2000
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1 Dynamics and statistics of a system of vortices (context) - Novikov - 1975
1 A renement of Wigner's semicircle law in a neighborhood of t.. (context) - Sinai, Soshnikov - 1998
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