Measurements of the Universal Constant in Kolmogoroff's Third Hypothesis for High Reynolds Number Turbulence

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Abstract
The viscous dissipation εr averaged over regions of size r is assumed log normal with variance σlogεr2 = A + μ log (L/r) in Kolmogoroff's third hypothesis, where A depends on the large scale motions, L is the energy scale of the turbulence ≫ r, and μ is a universal constant. The constant μ was measured from the slope of squared velocity derivative spectra using an expression derived by Yaglom. μ was also inferred from measurements of velocity derivative kurtosis K at various L/r values from the defining expression and the fact that σlog εr2 = log K for log normal εr, where r ≪ (ν3 / ε)1/4. An average value of 0.51 ± 0.02 was obtained from the spectral slopes over a 6:1 range of Reynolds number. A value of 0.44 ± 0.25 was indicated by the other method. Previous measurements range from 0.33 to 0.64.