Statistics of velocity gradients in turbulence at moderate Reynolds numbers
Open Access
- 1 February 1989
- journal article
- Published by IOP Publishing in Fluid Dynamics Research
- Vol. 4 (5-6) , 347-370
- https://doi.org/10.1016/0169-5983(89)90004-x
Abstract
A direct numerical simulation of the Navier-Stokes equation is performed in order to investigate the small scale structure of turbulence at moderately large microscale Reynolds numbers 40–140, using the spectral method with 3403 modes starting from a high-symmetric flow. It is shown that the small scale motion is statistically isotropic. The probability density distribution of the velocity is Gaussian, while those of the velocity gradients and the vorticity are not Gaussian but have long exponential tails. The moments of the velocity gradients are expressed in terms of the gamma function, and the ratio of the moments of the velocity gradients of successive orders increases linearly with the order. A comparison is made with a laboratory experiment.Keywords
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