Non-equilibrium Statistical Mechanics of Fluid Turbulence
Theory of fluid turbulence based on the non-equilibrium statistical mechanics is formulated using the infinite set of equations for the multi-point velocity distributions given by Lundgren (1967)  and Monin (1967)  and the cross − independence closure hypothesis proposed by Tatsumi (2001) . The present hypothesis is found to give identical closure to the distribution equations and hence the closed equations for the velocity distributions must be exact. This conclusion is confirmed by the fact that the moment-expansion of the distribution equations presents the equations for the mean velocity-products of various orders which are completely identical with the known equations derived from the Navier-Stokes equation directly. Another interesting result is that the energy-dissipation rate ε is expressed as an integral of the velocity-difference distribution which is mostly contributed from small-scale turbulence, making close analogy with the ‘fluctuation-dissipation theorem’ of non-equilibrium statistical mechanics.
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