Prandtl number effects on extreme mixing events in forced stratified turbulence
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 $Re := UL/ν\gg 1$ and Froude numbers $Fr :=(2πU)/(L N) \ll 1$, ($U$ and $L$ being characteristic velocity and length scales, $ν$ being 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 $Re_{b} := ε/(νN^{2}) \gg 1$ where $ε$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := ν/κ= \mathcal{O}(10)$ 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 $Re_{b}=50$, with resolutions up to $30240 \times 30240 \times 3780$. 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 $χ_0$) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$.