Implications of inertial subrange scaling for stably stratified mixing

Portwood, G. D.; de Bruyn Kops, S. M.; Caulfield, C. P.

doi:10.1017/jfm.2022.160

Implications of inertial subrange scaling for stably stratified mixing

Journal Article · Thu Mar 24 00:00:00 EDT 2022 · Journal of Fluid Mechanics

DOI:https://doi.org/10.1017/jfm.2022.160· OSTI ID:1879371

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Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of Massachusetts, Amherst, MA (United States)
Univ. of Cambridge (United Kingdom)

In this work, we investigate the effects of the turbulent dynamic range on active scalar mixing in stably stratified turbulence by adapting the theoretical passive scalar modelling and demonstrating their usefulness through consideration of the results of direct numerical simulations of statistically stationary homogeneous stratified and sheared turbulence. By analysis of inertial and inertial–convective subrange scalings, we show that the relationship between the active scalar and turbulence time scales is predicted by the ratio of the Kolmogorov and Obukhov–Corrsin constants, provided mean flow parameters permit the two subrange scalings to be appropriate approximations. We use the resulting relationship between time scales to parameterise an appropriate turbulent mixing coefficient $$\varGamma \equiv \chi /\epsilon$$, defined here as the ratio of available potential energy ($$E_p$$) and turbulent kinetic energy ($$E_k$$) dissipation rates. With the analysis presented here, we show that $$\varGamma$$ can be estimated by $$E_p,E_k$$ and a universal constant provided an appropriate Reynolds number is sufficiently high. This large Reynolds number regime appears here to occur at $$ {{Re_b}} \equiv \epsilon / \nu N^{2} \gtrapprox 300$$ where $$\nu$$ is the kinematic viscosity and $$N$$ is the characteristic buoyancy frequency. We propose a model framework for irreversible diapycnal mixing with robust theoretical parametrisation and asymptotic behaviour in this high-$$ {{Re_b}}$$ limit.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: US Army Research Laboratory (USARL); US Department of the Navy, Office of Naval Research (ONR); USDOE

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1879371

Report Number(s):: LA-UR-20-28841

Journal Information:: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 939; ISSN 0022-1120

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

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