Prandtl Number Effects on Extreme Mixing Events in Forced Stratified Turbulence

Abstract

`Strongly' stratified turbulent flows can self-organise into a  `layered anisotropic stratified turbulence' (LAST) regime, characterised by relatively deep and well-mixed density `layers' separated by relatively thin `interfaces' of enhanced density gradient. Understanding the associated mixing dynamics is important for parameterising heat transport in the world's oceans. It is challenging to study `LAST' mixing, as it is associated with Reynolds numbers Re := UL/ν  >> 1 and Froude numbers Fr :=(2πU)/(L N)  << 1, (U and L being characteristic velocity and length scales, ν being the kinematic viscosity and N the buoyancy frequency). As a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is still required, the buoyancy Reynolds number Reb := ε/(ν N2) >> 1 where ε is the TKE dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number Pr := ν /κ = O(10) in thermally-stratified water (where κ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude (Fr=0.5, 2) and Prandtl numbers (Pr=1, 7) forced so that Reb=50, with resolutions up to 30240 x 30240 x 3780. We find that, as Pr increases, emergent `interfaces' become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed `layers'. Nevertheless, `extreme' mixing events (with elevated local destruction rates of buoyancy variance χ0 dominating the total mixing budget) are still preferentially found in strongly stratified interfaces, which has significant implications for parameterising  diapycnal mixing in larger scale ocean models. This project received funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 956457 and used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. S.deB.K. was supported under U.S. Office of Naval Research Grant number N00014-19-1-2152.