Turbulence in a randomly stirred fluid

Abstract

The results of direct numerical simulations of a fluid stirred by the Gaussian random force 〈 fifj 〉 ∝k−3 are reported. It is shown that the mean properties of the random force generated turbulence are reasonably close to those observed in physical experiments. It is shown that higher-order moments of temporal and spatial velocity derivatives are dominated by different factors. It is shown that there is an intermediate range of wavenumbers with spatial and temporal spectra that fit E(k)∝k−5/3 and E(ω)∝ω−2. This suggests the breakdown of the random Taylor hypothesis in the inertial range of homogenous, isotropic turbulence at moderate Reynolds numbers.