FLUCTUATIONS IN THE IRREVERSIBLE DECAY OF TURBULENT ENERGY

A fluctuation law of the energy in freely decaying, homogeneous, and i sotropic turbulence is derived within standard closure hypotheses for three-dimensional incompressible flow. In particular, a fluctuation-di ssipation relation is derived which relates the strength of a stochast ic backscatter term in the energy decay equation to the mean of the en ergy dissipation rate. The theory is based on the so-called ''effectiv e action'' of the energy history and illustrates a Rayleigh-Ritz metho d recently developed to evaluate the effective action approximately wi thin probability density-function (PDF) closures. These effective acti ons generalize the Onsager-Machlup action of nonequilibrium statistica l mechanics to turbulent flow. They yield detailed, concrete predictio ns for fluctuations, such as multitime correlation functions of arbitr ary order, which cannot be obtained by direct PDF methods. They also c haracterize the mean histories by a variational principle.