Buoyancy-gradient mixing-length closure
= Buoyancy-gradient mixing-length closure
{title2=$K\sim d^2\sqrt{G_z}$}
For positive dense-fluid <reduced gravity> $G$ and upward coordinate $z$, an unstable gradient $G_z>0$ supplies buoyant work of order $d^2G_z$ over mixing length $d$. <velocity> $u\sim d\sqrt{G_z}$ and <eddy diffusivity> $K\sim ud$ follow. Order-one constants depend on the <turbulence> model. This closure is for an unstable gradient; its square root must not be applied to a stable negative gradient.