Velocity gradient distributions in fully developed turbulence: An experimental study

We report measurements of the probability distribution function of the velocity derivatives, and the corresponding hyperflatness factors, up to order 6, as a function of the microscale Reynolds number R-lambda. The measurements are performed in a flow produced between counter-rotating disks, using low-temperature helium gas as the working fluid, in a range of microscale Reynolds numbers lying between 150 and 2300. Consistently with previous studies, a transitional behavior is found around R(lambda)approximate to 700. We determine a simple scaling law, in terms of R-lambda, which allows the collapse of the tails of the pdf of the velocity derivatives onto a single curve, below the transition. We find well-defined relative power laws for the hyperflatness factors H-p and H-p*, throughout the entire range of variation of R-lambda:H-4 = F = (0.99+/-0.05)H-6(0.376+/-0.015) and H-5* = (0.95+/-0.05)H-6(0.67+/-0.022). These results are compared to those of previous investigators and to various theoretical approaches both statistical (multifractal model) and structural (i.e., based on a model of fine scales). (C) 1997 American Institute of Physics. [S1070-6631(97)01612-7].