Statistics of velocity gradients in turbulence at moderate Reynolds numbers
Abstract
A direct numerical simulation of the NavierStokes equation is performed in order to investigate the small scale structure of turbulence at moderately large microscale Reynolds numbers 40140, using the spectral method with 340 ^{3} modes starting from a highsymmetric 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.
 Publication:

Fluid Dynamics Research
 Pub Date:
 February 1989
 DOI:
 10.1016/01695983(89)90004X
 Bibcode:
 1989FlDyR...4..347K
 Keywords:

 Statistical Analysis;
 Turbulent Flow;
 Velocity Distribution;
 Computerized Simulation;
 NavierStokes Equation;
 Probability Density Functions;
 Reynolds Number;
 Fluid Mechanics and Heat Transfer