On the Shear Number Effect in Stratified Shear Flow

The influence of the shear number on the turbulence evolution in a stably stratified fluid is investigated using direct numerical simulations on grids with up to 512 × 256 × 256 points. The shear number SK/ε is the ratio of a turbulence time scale K/ε to the shear time scale 1/S. Simulations are performed at two initial values of the Reynolds number Re _Λ= 44.72 and Re _Λ= 89.44. When the shear number is increased from small to moderate values, the nondimensional growth rate γ= (1/SK)dK/dt of the turbulent kinetic energy K increases since the shear forcing and its associated turbulence production is larger. However, a further increase of the shear number from moderate to large values results in a reduction of the growth rate γ and the turbulent kinetic energy K shows long-time decay for sufficiently large values of the shear number. The inhibition of turbulence growth at large shear numbers occurs for both initial values of the Reynolds number and can be explained with the predominance of linear effects over nonlinear effects when the shear number is sufficiently high. It is found that, at the higher initial value of the Reynolds number, the reduction of the growth rate occurs at a higher value of the shear number. The shear number is found to affect spectral space dynamics. Turbulent transport coefficients decrease with increasing shear number. Received 23 June 1998 and accepted 25 February 1999