# Scalar mixing patterns in forced simulations of stratified turbulence: the importance of extreme events - Miles Couchman

TUR - Mathematical aspects of turbulence: where do we stand?

Understanding the degree to which turbulence enhances the irreversible mixing of scalars in density-stratified fluids is a central problem in geophysical fluid dynamics. An outstanding area of uncertainty involves determining whether local properties of the velocity field, such as the turbulent dissipation rate of kinetic energy $\epsilon$, may be reliably used to predict local mixing rates, as measured by the dissipation rate of scalar variance $\chi$. In parametrizations of ocean turbulence, for example, distributions of $\epsilon$ and $\chi$ are assumed to be directly correlated, yielding a constant mixing coefficient $\Gamma = \chi / \epsilon$, although such an assumption has been heavily questioned. We here probe local correlations between $\epsilon$ and $\chi$ by considering direct numerical simulations of stratified turbulence in a triply-periodic domain with an initially linear density gradient and bulk properties held in steady state by a large-scale background forcing, similar to simulations considered by Portwood et al (JFM 2016) and Taylor et al (JPO 2019). We first demonstrate that the forcing gives rise to a previously unreported vortex structure that induces shearing currents in the surrounding flow These shearing layers are found to be correlated with sharp interfaces in the perturbed density field, characterized by a significantly elevated mixing coefficient $\Gamma$ and contributing substantially to the total amount of mixing within the domain, despite being under-represented in volume. Thus, while the majority of the domain is indeed characterized by the canonical mixing coefficient $\Gamma = 0.2$ often assumed in oceanographic models, it is relatively rare, but extreme mixing events that dominate the bulk mixing rates, a phenomenon also recently identified in observational oceanographic measurements  by Couchman et al. (GRL, 2021). Our findings emphasize that $\chi$ and $\epsilon$ contain independent information about mixing processes and should thus be considered in tandem, and suggest that current parametrizations of oceanic heat transport may be skewed by undersampling, capturing the most common but not necessarily the most important mixing events.

This talk is part of the Isaac Newton Institute Seminar Series series.