Reynolds number dependence of velocity structure functions in turbulent shear flows

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Abstract
Moments, up to order eight, of the structure function of the steamwise velocity fluctuation, have been measured in both laboratory and atmospheric turbulent shear flows. The Reynolds number dependence of structure functions evaluated for a separation equal to the Taylor microscale is closely approximated by both lognormal and β models, at least for moments up to order six. Both models predict identical inertial subrange behavior for the sixth‐order structure functions. This prediction is in good agreement with experiment when the value of 0.2 is used for the universal exponent μ. This value has been obtained from correlations of the squared velocity derivative fluctuations, calculated for both laboratory and atmospheric measurements over the inertial subrange. The slope of the correlation is related to that of the sixth‐order structure function, in agreement with a conjecture by Frisch, Sulem, and Nelkin. When plotted against moments of order n+2, moments of even order n exhibit a power‐law behavior whose exponent is in closer agreement with the lognormal than the β model.