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Velocity gradient distributions in fully developed turbulence: An experimental study

1997; American Institute of Physics; Volume: 9; Issue: 12 Linguagem: Inglês

10.1063/1.869484

1527-2435

F. Belin, J. Maurer, P. Tabeling, H. Willaime,

Wind and Air Flow Studies

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 Rλ. 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 Rλ≈700. We determine a simple scaling law, in terms of Rλ, 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 Hp and Hp*, throughout the entire range of variation of Rλ: H4=F=(0.99±0.05)H60.376±0.015 and H5*=(0.95±0.05)H60.67±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).