Turbulence Fluctuations and New Universal Realizability Conditions in Modelling
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 a priori the poor predictions of PDF closures even when the classical 2nd-order moment realizability conditions are satisfied.
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