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 $$Re := UL/\nu \gg 1$$ and Froude numbers $$Fr :=(2{\rm \pi} U)/(L N) \ll 1$$ ( $$U$$ and $$L$$ being characteristic velocity and length scales, $$\nu$$ 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 $$Re_{b} := \epsilon /(\nu N^{2}) \gg 1$$ , where $$\epsilon$$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $$Pr := \nu /\kappa = {O}(10)$$ in thermally stratified water (where $$\kappa$$ 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 $$Re_{b}=50$$ , with resolutions up to $$30\,240 \times 30\,240 \times 3780$$ . 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 $$\chi _0$$ ) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $$Pr$ .
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC05-00OR22725
- OSTI ID:
- 2323351
- Alternate ID(s):
- OSTI ID: 2581371
- Journal Information:
- Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 983; ISSN 0022-1120
- Publisher:
- Cambridge University Press (CUP)Copyright Statement
- Country of Publication:
- United Kingdom
- Language:
- English
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