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Mixing in a Moderately Sheared Salt-Fingering Layer

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  • 1 College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon
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Abstract

Mixing due to sheared salt fingers is studied by means of direct numerical simulations (DNS) of a double-diffusively unstable shear layer. The focus is on the “moderate shear” case, where shear is strong enough to produce Kelvin–Helmholtz (KH) instability but not strong enough to produce the subharmonic pairing instability. This flow supports both KH and salt-sheet instabilities, and the objective is 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, as well as 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; however, 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 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. Shear therefore reduces mixing, despite providing an additional energy source. The dissipation ratio Γ is near 0.2 for shear-dominated cases but is 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.

Corresponding author address: W. D. Smyth, College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331-5503. E-mail: smyth@coas.oregonstate.edu

Abstract

Mixing due to sheared salt fingers is studied by means of direct numerical simulations (DNS) of a double-diffusively unstable shear layer. The focus is on the “moderate shear” case, where shear is strong enough to produce Kelvin–Helmholtz (KH) instability but not strong enough to produce the subharmonic pairing instability. This flow supports both KH and salt-sheet instabilities, and the objective is 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, as well as 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; however, 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 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. Shear therefore reduces mixing, despite providing an additional energy source. The dissipation ratio Γ is near 0.2 for shear-dominated cases but is 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.

Corresponding author address: W. D. Smyth, College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331-5503. E-mail: smyth@coas.oregonstate.edu
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