Gl. Eyink et Fj. Alexander, TURBULENCE FLUCTUATIONS AND NEW UNIVERSAL REALIZABILITY CONDITIONS INMODELING, Physical review letters, 78(13), 1997, pp. 2563-2566
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.