Direct numerical simulations of turbulence with confinement and rotation

Abstract

The goal of this work is to analyse how solid body rotation affects forced turbulence enclosed within solid boundaries, and to compare it to results of the experiment performed by Hopfinger et al. (1982). In order to identify various mechanisms associated with rotation, confinement, and forcing, a numerical pseudo-spectral code is used for performing direct numerical simulations. The geometry is simplified with respect to the experimental one. First, we are able to reproduce the linear regime, as propagating inertial waves that undergo reflections at the walls. Second, the Ekman pumping phenomenon, proportional to the rotation rate, is identified in freely decaying turbulence, for which the evolution of the flow bounded by walls is compared to the evolution of unbounded homogeneous turbulence. Finally we introduce a local forcing on a plane in physical space, for simulating the effect of an oscillating grid, so that diffusive turbulence is created, and we examine the structuring of the flow under the combination of the linear and nonlinear mechanisms. A transition to an almost two-dimensional state is shown to occur between the region close to the forcing and an outer region in which vortices appear, the number of which depends on the Reynolds and Rossby numbers. In this region, the anisotropy of turbulence is examined, and the numerical predictions are shown to reproduce many of the most important features present in the experimental flow.