Mixing efficiency in stratified turbulence

• We consider mixing of the density field in stratified turbulence and argue that, at sufficiently high Reynolds numbers, stationary turbulence will have a mixing efficiency and closely related mixing coefficient described solely by the turbulent Froude number (Formula presented.), where (Formula presented.) is the kinetic energy dissipation, (Formula presented.) is a turbulent horizontal velocity scale and (Formula presented.) is the Brunt–Väisälä frequency. For (Formula presented.), in the limit of weakly stratified turbulence, we show through a simple scaling analysis that the mixing coefficient scales as (Formula presented.), where (Formula presented.) and (Formula presented.) is the potential energy dissipation. In the opposite limit of strongly stratified turbulence with (Formula presented.), we argue that (Formula presented.) should reach a constant value of order unity. We carry out direct numerical simulations of forced stratified turbulence across a range of (Formula presented.) and confirm that at high (Formula presented.), (Formula presented.), while at low (Formula presented.) it approaches a constant value close to (Formula presented.). The parametrization of (Formula presented.) based on (Formula presented.) due to Shih et al. (J. Fluid Mech., vol. 525, 2005, pp. 193–214) can be reinterpreted in this light because the observed variation of (Formula presented.) in their study as well as in datasets from recent oceanic and atmospheric measurements occurs at a Froude number of order unity, close to the transition value (Formula presented.) found in our simulations.

Ämnesord

NATURVETENSKAP  -- Fysik -- Annan fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Other Physics Topics (hsv//eng)

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mixing and dispersion

ocean processes

stratified turbulence

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