A renormalized expression for the turbulent energy dissipation rate

Abstract

Conditional elimination of degrees of freedom is shown to lead to an exact expression for the rate of turbulent energy dissipation in terms of a renormalized viscosity and a correction. The correction is neglected on the basis of a previous hypothesis [W.D. McComb and C. Johnston, J.Phys.A v33 L15 (2000)] that there is a range of parameters for which a quasi-stochastic estimate is a good approximation to the exact conditional average. This hypothesis was tested by a perturbative calculation to second order in the local Reynolds number, and the Kolmogorov prefactor (taken as a measure of the renormalized dissipation rate) was found to reach a fixed point which was insensitive to initial values of the kinematic viscosity and to values of the spatial rescaling factor h in the range 0.4 <= h <= 0.8.