Kinematic Effects of Differential Transport on Mixing Efficiency in a Diffusively Stable, Turbulent Flow

Abstract

If temperature and salinity are mixed at different rates, the mixing efficiencies in flows with the same stratification and forcing can vary if the contributions of temperature and salinity to the density differ. Two models are used to examine the effect of differential transport of salt and heat on the mixing efficiency. The first model assumes constant eddy diffusivities for heat and salt and examines the effect of the density ratio R? = α?T/??S and the diffusivity ratio d = KS/KT on the mixing efficiency. The model predicts that the effect of differential transport can be as large as that due to stratification and the type of process generating the turbulence. The second model incorporates the effect of stratification on the mixing by using results from laboratory experiments on entrainment across a sharp density interface. The model predicts that the mixing efficiency depends on the density ratio and a Richardson number Ri0 based on the density jump and velocity and length scales of the turbulence near the interface. Because the laboratory measurements show that salt and heat are entrained at equal rates for Richardson numbers less than a transition value Ric, the mixing efficiency initially increases with increasing Ri0 for all density ratios. However, for Ri0 > Ric, the efficiency decreases (past a peak at Ric) for low density ratio and increases monotonically for high density ratio. These results suggest that the generation of fine structure in diffusively stable regions of the ocean can depend on the density ratio.