Turbulence Fluctuations and New Universal Realizability Conditions in Modelling
arXiv:chao-dyn/9607014 · doi:10.1103/PhysRevLett.78.2563
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.
4 pages, LaTeX (Version 2.09), 3 figures, Postscript, Submitted to Phys. Rev. Lett