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Title: Is the flux coefficient of stratified turbulence a universal constant?
Plain: 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: 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.
Settled by: 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 $\Gamma(\mathrm{Re}_{b}, \mathrm{Ri})$.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: contested
Status note: Laboratory, DNS and ocean estimates range from below 0.1 to above 0.3 depending on forcing, $\mathrm{Re}_{b}$ and Pr.
Posed since: 1980