Velocity gradient distributions in fully developed turbulence: An experimental study

• Published in: Physics of fluids (1994) 1997-12, Vol.9 (12), p.3843-3850
• Main Authors: Belin, F., Maurer, J., Tabeling, P., Willaime, H.
• Format: Article
• Language: English
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.869484

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 λ . 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 λ ≈700. We determine a simple scaling law, in terms of R λ , 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 λ : 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).