Turbulence renormalization group calculations using statistical mechanics methods

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Abstract
The renormalizationgroup theory of fluid turbulence is developed from a statistical mechanical viewpoint using an exact expression for the functional probability distribution of the velocity field. The latter is similar in form to an equilibrium Gibbs distribution, and is derived by combining Lagrangianstatistical mechanics with an Eulerian fluid description. It is shown that this distribution enables an RG transformation to be defined, evaluated, and analyzed using statistical mechanical techniques. The method of determining amplitudes used here also differs from previous work, in that the indeterminacy of the relevant stirring force parameters is resolved through the essential requirement that all coarse‐grained distributions must yield the actual dissipation rate E. Consequently, although the fixed point solutions of the dynamic RG approach are recovered, slightly different numerical results are obtained for amplitudes. The present approach yields, for example, for Kolmogorov’s constant, C K=1.44.