Turbulence Fluctuations and New Universal Realizability Conditions in Modelling
chao-dyn
2009-10-28 v1 Chaotic Dynamics
Abstract
General turbulent mean statistics are shown to be characterized by a variational principle. The variational functionals, or ``effective actions'', have experimental consequences for turbulence fluctuations and are subject to realizability conditions of positivity and convexity. An efficient Rayleigh-Ritz algorithm is available to calculate approximate effective actions within PDF closures. Examples are given for Navier-Stokes and for a 3-mode system of Lorenz. The new realizability conditions succeed at detecting {\em a priori} the poor predictions of PDF closures even when the classical 2nd-order moment realizability conditions are satisfied.
Keywords
Cite
@article{arxiv.chao-dyn/9607014,
title = {Turbulence Fluctuations and New Universal Realizability Conditions in Modelling},
author = {Gregory L. Eyink and Francis J. Alexander},
journal= {arXiv preprint arXiv:chao-dyn/9607014},
year = {2009}
}
Comments
4 pages, LaTeX (Version 2.09), 3 figures, Postscript, Submitted to Phys. Rev. Lett