Prandtl number effects on extreme mixing events in forced stratified turbulence

Abstract

Relatively strongly stratified turbulent flows tend to 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 a central problem in geophysical fluid dynamics. It is challenging to study LAST mixing, as it is associated with Reynolds numbers Re := UL/ν ≫ 1 and Froude numbers Fr := (2πU)/(LN) ≪ 1 (U and L being characteristic velocity and length scales, ν the kinematic viscosity and N the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number Reb := ε/(νN2) ≫ 1, where ε is the (appropriately volume-averaged) turbulent kinetic energy 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 (Pr = 1, 7) numbers forced so that Reb = 50, with resolutions up to 30 240 × 30 240 × 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’. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance χ0) are always preferentially found in the (statically stable) interfaces, irrespective of the value of Pr.