Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1996-07-26
Nonlinear Sciences
Chaotic Dynamics
4 pages, LaTeX (Version 2.09), 3 figures, Postscript, Submitted to Phys. Rev. Lett
Scientific paper
10.1103/PhysRevLett.78.2563
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.
Alexander Francis J.
Eyink Gregory L.
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