Turbulence in a sheared , salt - fingering - favorable environment : 1 Anisotropy and effective diffusivities

5 Direct numerical simulations (DNS) of a shear layer with salt-fingering-favorable stratifica6 tion have been performed for different Richardson numbers Ri and density ratios Rρ. When 7 the Richardson number is infinite (unsheared case), the primary instability is square plan8 form salt-fingering, alternating cells of rising and sinking fluid. In the presence of shear, 9 salt-fingering takes the form of salt sheets, planar regions of rising and sinking fluid, aligned 10 parallel to the sheared flow. After the onset of secondary instability, the flow becomes 11 turbulent; however, our results indicate that the continued influence of the primary insta12 bility biases estimates of the turbulent kinetic energy dissipation rate. Thermal and saline 13 buoyancy gradients become more isotropic than the velocity gradients at dissipation scales. 14 Estimates of the turbulent kinetic energy dissipation rate by assuming isotropy in the ver15 tical direction can underestimate its true value by a factor of 2 to 3, whereas estimates of 16 thermal and saline dissipation rates are relatively accurate. Γ approximated by assuming 17 isotropy agrees well with observational estimates, but is larger than the true value of Γ by 18 approximated a factor of 2. The transport associated with turbulent salt sheets is quanti19 fied by thermal and saline effective diffusivities. Salt sheets are ineffective at transporting 20 momentum. Thermal and saline effective diffusivities decrease with decreasing Ri, despite 21 the added energy source provided by background shear. Nondimensional quantities, such as 22 thermal to saline flux ratio, are close to the predictions of linear theory. 23