Measurements of the Small-Scale Structure of Turbulence at Moderate Reynolds Numbers

Measurements of probability densities and distributions, moments, and spectra obtained from the first two time derivatives of the streamwise velocity fluctuation in a mixing layer are presented. Probability distributions of squared derivatives are found to be nearly log normal. The skewness $\mathrm{(S)}$ and kurtosis $\mathrm{(K)}$ of the first derivative are compared with new atmospheric data at much higher Reynolds numbers. Reynolds-number dependence is indicated, in conflict with universal equilibrium theory. A modified theory using fluctuating dissipation predicts that $S$ and $K$ have power-law behavior with turbulent Reynolds number and are related by ${\mathrm{S\hspace{0.17em}\propto \hspace{0.17em}K}}^{\text{3/8}}$ , in general agreement with the trends of the limited data available.