Mixing in a moderately sheared, diffusively unstable layer

We study mixing in a thermohaline staircase by means of direct numerical simulations (DNS). A single saltfingering layer is modeled as a diffusively unstable shear layer of hyperbolic tangent form. Our main interest is the influence of shear, and we focus on what we call the “moderate shear” case. This is the regime where shear is strong enough to produce Kelvin-Helmholtz (KH) instability, but not to produce the subharmonic pairing instability. This flow supports both KH and salt sheet instabilities, and we wish to see how the two mechanisms work together to flux heat, salt and momentum across the layer. For observed values of the bulk Richardson number Ri and the density ratio Rρ, the linear growth rates of KH and salt sheet instabilities are similar. These mechanisms, and their associated secondary instabilities, lead the flow to a fully turbulent state. Depending on the values of Ri and Rρ, the resulting turbulence may be driven mainly by shear or mainly by salt fingering. Turbulent mixing causes the profiles of temperature, salinity and velocity to spread but, in salt sheet dominated cases, the net density (or buoyancy) layer thins over time. This could be a factor in the maintenance of the staircase and is also an argument in favor of an eventual role for Holmboe instability. Fluxes are scaled using both laboratory scalings for a thin layer and more common parameterizations via an effective diffusivity. Fluxes are generally stronger in salt sheet-dominated cases. Shear instability disrupts salt sheet fluxes while adding little flux of its own. The dissipation ratio Γ is near 0.2 for shear-dominated cases but much larger when salt sheets are dominant, supporting the use of Γ in the diagnosis of observed mixing phenomena. The profiler approximation Γz , however, appears to significantly overestimate the true dissipation ratio. We close with suggestions for explorations of more energetic regimes that will be possible in the near future as petascale computers become available.