  A fluctuation law of the energy in freely-decaying, homogeneous and isotropic
turbulence is derived within standard closure hypotheses for 3D incompressible
flow. In particular, a fluctuation-dissipation relation is derived which
relates the strength of a stochastic backscatter term in the energy decay
equation to the mean of the energy dissipation rate. The theory is based on the
so-called ``effective action'' of the energy history and illustrates a
Rayleigh-Ritz method recently developed to evaluate the effective action
approximately within probability density-function (PDF) closures. These
effective actions generalize the Onsager-Machlup action of nonequilibrium
statistical mechanics to turbulent flow. They yield detailed, concrete
predictions for fluctuations, such as multi-time correlation functions of
arbitrary order, which cannot be obtained by direct PDF methods. They also
characterize the mean histories by a variational principle.
