Effect of the shear parameter on velocity-gradient statistics in homogeneous turbulent shear flow

Abstract

The effect of the shear parameter on the small-scale velocity statistics in an homogeneous turbulent shear flow is investigated using direct numerical simulations (DNSs) of the incompressible Navier–Stokes equations on a 5123 grid. We use a novel pseudo-spectral algorithm that allows us to set the initial value of the shear parameter in the range 3–30 without the shortcomings of previous numerical approaches. We find that the tails of the probability distribution function of components of the vorticity vector and rate-of-strain tensor are progressively distorted with increasing shear parameter. Furthermore, we show that the shear parameter has a direct effect on the structure of the vorticity field, which manifests through changes in its alignment with the eigenvectors of the rate-of-strain tensor. We also find that increasing the shear parameter causes the main contribution to enstrophy production to shift from the nonlinear terms to the rapid terms (terms that are proportional to the mean shear) due to the aforementioned changes in the alignment. We attempt to explain these trends using viscous rapid distortion theory; however, while the theory does capture some effects of the shear parameter, it fails to predict the correct dependence on Reynolds number. Comparisons with recent experiments are also shown. The trends predicted by the DNS and the experiments are in good agreement. Moreover, the prefactors in the Reynolds number scaling laws for the skewness and flatness of the longitudinal velocity derivative are shown to have a statistically significant dependence on the shear parameter.