Acceleration of Horizontal Mean Currents in DNS of Stratified Turbulent Shear Flows

Abstract

We present some results and comments on DNS of freely decaying horizontal parallel flows when initially affected by a turbulent velocity field in a strongly stratified fluid. Turbulent shear flows in stratified media have already been simulated by Jacobitz et al. [2] for instance. Experiments have been carried out in a thermally stratified wind tunnel by Piccirillo et al. [3]. However, these numerical and experimental studies generally focus on the influence of a horizontal mean flow on the stratified turbulence. In the present paper, we focus on the accelerating effect of stratified turbulence onto the horizontal mean flow. We solve the 3D Navier-Stokes equations under the Boussinesq approximation with a pseudo-spectral direct simulation code (O. Thual [4]). The flow evolves in a periodic cubic box with no external forcing, the initial condition being the sum of a horizontal parallel flow \( \vec U \)(z, 0) in the x-direction and a homogeneous, isotropic turbulent velocity field \( \vec{u}' \) (x, y, z, 0). The Reynolds number is 67 initially (based on the rms value u 0 of u’, the integral lengthscale l and the kinematic viscosity). We choose \( \vec{U} \) (z,0) as a cosine with amplitude U 0 and a wavelength equal to the size of the box L b . The value of U 0 is chosen such that the mean flow energy is initially one third of the total energy. In the stratified case, the Prandtl number is taken equal to unity and there is no potential energy initially. The initial Froude number Fr = u 0 /Nl (where N is the Brunt-Väisälä pulsation) is 0.13. Such a low value is typical of strongly stratified turbulence.