Is the flux coefficient of stratified turbulence a universal constant?
In plain words
When turbulence stirs water layered by temperature or salt, part of its energy lifts heavy fluid and mixes the layers and the rest turns into heat. Ocean models assume that a fixed fraction (about one sixth) goes into mixing, but measurements scatter widely.
Precise statement
Define the flux coefficient $\Gamma = B/\epsilon$ ($B$ buoyancy flux, $\epsilon$ kinetic-energy dissipation rate), set to 0.2 in ocean parameterizations (Osborn 1980). Determine $\Gamma$ as a function of buoyancy Reynolds number $\mathrm{Re}_b = \epsilon/(\nu N^2)$ ($N$ buoyancy frequency), gradient Richardson number Ri and Prandtl number Pr for stationary stratified shear turbulence, including whether $\Gamma$ tends to a constant as $\mathrm{Re}_b \to \infty$ at fixed Ri.
What would settle it
DNS and laboratory experiments at $\mathrm{Re}_{b} > 10^{3}$ with $\mathrm{Pr} \sim 7$ and $\text{Schmidt number} \sim 700$ (heat and salt) mapping $\Gamma(\mathrm{Re}_{b}, \mathrm{Ri})$.
Status in the literature
Laboratory, DNS and ocean estimates range from below 0.1 to above 0.3 depending on forcing, $\mathrm{Re}_{b}$ and Pr.
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