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.Comment: 4 pages, LaTeX (Version 2.09), 3 figures, Postscript, Submitted to
Phys. Rev. Let