Parametric Dependence of Homogeneous Turbulent Shear Flow on Reynolds Number and Shear Parameter

The combined role of the Shear Parameter, $S^{*} = S k / \epsilon$, and the Reynolds number in homogeneous turbulent shear flow is studied using direct numerical simulations (DNS). The parametric investigation involves DNS of $256^{3}$, $512^{3}$ and $1024^{3}$ with a constant shear parameter, $S^{*}$, between 1 and 100. Particular attention is given to velocity derivatives (strain and rotation) and higher-order structure functions and their scaling with the two parameters. This study is in line with some recent results reported by Schumacher, [Phys. Fluids 16, 2004]. Due to the high level of shear investigated, a new algorithm that avoids the remeshing step is used. The 20\% - 40\% loss in kinetic energy and dissipation rate reported by Lee \emph{et al.} [JFM, 216, 1990] using the Rogallo code is consequently avoided.