Mixing across stable density interfaces in forced stratified turbulence

Abstract

Understanding how turbulence enhances irreversible scalar mixing in density-stratified fluids is a central problem in geophysical fluid dynamics. While isotropic overturning regions are commonly the focus of mixing analyses, we here investigate whether significant mixing may arise in anisotropic statically-stable regions of the flow. Focusing on a single forced direct numerical simulation of stratified turbulence, we analyze spatial correlations between the vertical density gradient $\partialρ/\partial z$ and the dissipation rates of kinetic energy $ε$ and scalar variance $χ$, the latter quantifying scalar mixing. The domain is characterized by relatively well-mixed density layers separated by sharp stable interfaces that are correlated with high vertical shear. While static instability is most prevalent within the mixed layers, much of the scalar mixing is localized to the intervening interfaces, a phenomenon not apparent if considering local static instability or $ε$ alone. While the majority of the domain is characterized by the canonical flux coefficient $Γ\equivχ/ε=0.2$, often assumed in ocean mixing parameterizations, extreme values of $χ$ within the statically-stable interfaces, associated with elevated $Γ$, strongly skew the bulk statistics. Our findings suggest that current parameterizations of turbulent mixing may be biased by undersampling, such that the most common, but not necessarily the most significant, mixing events are overweighted. Having focused here on a single simulation of stratified turbulence, it is hoped that our results motivate a broader investigation into the role played by stable density interfaces in mixing, across a wider range of parameters and forcing schemes representative of ocean turbulence.