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A renormalized expression for the turbulent energy dissipation rate

C. Johnston·W. D. McComb
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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.

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C. Johnston, W. D. McComb. 2000-12-13. A renormalized expression for the turbulent energy dissipation rate. https://doi.org/10.1103/physreve.63.015304

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