Frank Jacobitz
Department of Mechanical Engineering, University of California, Riverside, USA

Direct Numerical Simulations of turbulence in stratified shear flows

Shear and stratification are ubiquitous features of turbulent flow in the atmosphere and oceans. The prototypical example of this flow with uniform vertical shear dU/dz and uniform vertical density stratification drho/dz has been studied extensively in the past from the pioneering work by G.I.
Taylor in 1914 to numerous experimental and numerical investigations in the last decade.

This study considers two different stratified shear flows. In the first flow, the effect of uniform horizontal shear dU/dy on the turbulence evolution is investigated. In horizontal shear flow, a higher turbulence level and stronger mixing have been observed compared to vertical shear
flow with the same magnitude of shear and stratification. This can be explained with a reduced influence of buoyancy on the turbulence production mechanism. Horizontal shear has been observed in geophysical flow over topography and in frontal systems.

In the second flow, shear due to a variation of the velocity direction as opposed to a variation of the velocity magnitude is considered. Here, the mean velocity describes a spiral in the vertical direction. The overall shear rate is matched to that of a uniform shear flow case. A similar turbulence evolution is observed as long as the integral scale of the turbulent motion is small compared to the length of the velocity spiral. Such flows have been observed in the atmosphere and the oceans.

The stratified shear flows are studied using direct numerical simulations. In the direct numerical approach, all dynamically important scales of the velocity and density fields are resolved. A spectral method is used for the spatial discretization and the simulations are advanced in time with
a fourth-order Runge-Kutta scheme. The simulations are performed on a parallel computer using up to 512 x 256 x 256 grid points.