LES computations and comparison with Kolmogorov theory for two-point pressure–velocity correlations and structure functions for globally anisotropic turbulence

Abstract

A new extension of the Kolmogorov theory, for the two-point pressure–velocity correlation, is studied by LES of homogeneous turbulence with a large inertial subrange in order to capture the high Reynolds number nonlinear dynamics of the flow. Simulations of both decaying and forced anisotropic homogeneous turbulence were performed. The forcing allows the study of higher Reynolds numbers for the same number of modes compared with simulations of decaying turbulence. The forced simulations give statistically stationary turbulence, with a substantial inertial subrange, well suited to test the Kolmogorov theory for turbulence that is locally isotropic but has significant anisotropy of the total energy distribution. This has been investigated in the recent theoretical studies of Lindborg (1996) and Hill (1997) where the role of the pressure terms was given particular attention. On the surface the two somewhat different approaches taken in these two studies may seem to lead to contradictory conclusions, but are here reconciled and (numerically) shown to yield an interesting extension of the traditional Kolmogorov theory. The results from the simulations indeed show that the two-point pressure–velocity correlation closely adheres to the predicted linear relation in the inertial subrange where also the pressure-related term in the general Kolmogorov equation is shown to vanish. Also, second- and third-order structure functions are shown to exhibit the expected dependences on separation.