Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1996-09-27
Phys. Rev. E 56 (1997) 5413-5422
Nonlinear Sciences
Chaotic Dynamics
26 pages, Latex Version 2.09, plus seceq.sty, a stylefile for sequential numbering of equations by section. This version inclu
Scientific paper
10.1103/PhysRevE.56.5413
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.
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