An exact expression for the Reynolds number dependence of the energy dissipation rate in homogeneous, isotropic turbulence

TL;DR

This paper derives an exact expression for how the energy dissipation rate in homogeneous, isotropic turbulence depends on the Reynolds number, using the Karman-Howarth equation and numerical simulation data.

Contribution

It provides a new exact formula linking the dissipation rate to the Reynolds number based on the Karman-Howarth equation, with a constant coefficient determined from simulations.

Findings

Coefficient in the formula is effectively constant across simulations.

Derived expression matches numerical data well.

Enhances understanding of turbulence energy dissipation dependence.

Abstract

The Reynolds number dependence of the dimensionless dissipation rate is derived directly from the Karman-Howarth equation in terms of the inverse of the integral scale Reynolds number and a coefficient which depends on the second- and third-order structure functions. Fitting this form to the results from a direct numerical simulation indicates that the coefficient is effectively constant.