TURBULENCE FLUCTUATIONS AND NEW UNIVERSAL REALIZABILITY CONDITIONS INMODELING

General turbulent mean statistics are shown to be characterized by a v ariational principle. The variational functionals, or ''effective acti ons,'' have experimental consequences for turbulence fluctuations and are subject to realizability conditions of positivity and convexity. A n efficient Rayleigh-Ritz algorithm is available to calculate approxim ate effective actions within probability density function (PDF) closur es. Examples are given for Navier-Stokes and for a three-mode system o f Lorenz. The new realizability conditions succeed at detecting a prio ri the poor predictions of PDF closures even when the classical second -order moment realizability conditions are satisfied.