Methods for measuring energy dissipation rate in anisotropic turbulence

TL;DR

This paper derives mathematically precise relationships between energy dissipation rate and measurable velocity structure functions in anisotropic turbulence, aiding experimental measurements across various flow conditions.

Contribution

It provides exact relationships based on Navier-Stokes equations for anisotropic turbulence, including approximate forms under local stationarity and homogeneity assumptions.

Findings

Derived exact relationships for anisotropic turbulence energy dissipation.

Provided approximate formulas valid for arbitrary Reynolds numbers.

Clarified mathematical considerations for experimental application.

Abstract

Energy dissipation rate is an important parameter for nearly every experiment on turbulent flow. Mathematically precise relationships between energy dissipation rate and other measurable statistics for the case of anisotropic turbulence are useful to experimentalists. Such relationships are obtained for which the measurable statistics are the 3rd-order and 2nd-order velocity structure functions as well as the acceleration-velocity structure function. The relationships are derived using the Navier-Stokes equation without approximation. Approximate versions are obtained on the basis of local stationarity and local homogeneity. The latter are valid for arbitrary Reynolds numbers for the case of stationary, homogeneous turbulence. Precise use of the mathematics requires care noted in the Discussion section.