The effect of nonvertical shear on turbulence in a stably stratified medium

Abstract

Direct numerical simulations were performed in order to investigate the evolution of turbulence in a stably stratified fluid forced by nonvertical shear. Past research has been focused on vertical shear flow, and the present work is the first systematic study with vertical and horizontal components of shear. The primary objective of this work was to study the effects of a variation of the angle θ between the direction of stratification and the gradient of the mean streamwise velocity from θ=0, corresponding to the well-studied case of purely vertical shear, to θ=π/2, corresponding to purely horizontal shear. It was observed that the turbulent kinetic energy K evolves approximately exponentially after an initial phase. The exponential growth rate γ of the turbulent kinetic energy K was found to increase nonlinearly, with a strong increase for small deviations from the vertical, when the inclination angle θ was increased. The increased growth rate is due to a strongly increased turbulence production caused by the horizontal component of the shear. The sensitivity of the flow to the shear inclination angle θ was observed for both low and high values of the gradient Richardson number Ri, which is based on the magnitude of the shear rate. The effect of a variation of the inclination angle θ on the turbulence evolution was compared with the effect of a variation of the gradient Richardson number Ri in the case of purely vertical shear. An effective Richardson number Rieff was introduced in order to parametrize the dependence of the turbulence evolution on the inclination angle θ with a simple model based on mean quantities only. It was observed that the flux Richardson number Rif depends on the gradient Richardson number Ri but not on the inclination angle θ.