Probability density functions, skewness, and flatness in large Reynolds number turbulence

Abstract

Probability density functions (PDF) of longitudinal velocity increments are measured in an experiment using low temperature helium gas, in which a large domain of microscale Reynolds numbers ${\mathit{R}}_{\ensuremath{\lambda}}$ (from 150 to 5040) is explored. The technique of measurement, which is essentially hot wire anemometry, but operating in nonstandard conditions, is described. In the inertial range of scales, and for a given scale of separation, the PDF are found to be independent of the Reynolds number at large ${\mathit{R}}_{\ensuremath{\lambda}}$. Measurements of the skewness and the flatness of the velocity derivatives are performed in a range of ${\mathit{R}}_{\ensuremath{\lambda}}$ lying between 150 and 3200. The surprising result that we find is that these quantities first increase with the Reynolds number up to ${\mathit{R}}_{\ensuremath{\lambda}}$\ensuremath{\approxeq}700 and then cease to increase further, indicating a transitional behavior. \textcopyright{} 1996 The American Physical Society.