= Fixed-energy turbulent mixed layer
{title2=$u^2h=A\Omega^2R^3$}
In a slowly deepening mixed layer driven by a rotating boundary, a phenomenological balance between <energy> input, turbulent loss and <acceleration> of entrained <fluid> can keep total <kinetic energy> approximately fixed. For a tank of radius $R$ this gives $u^2h=A\Omega^2R^3$, so <velocity> decreases as $h^{-1/2}$. The closure does not make the speed constant and is an additional physical assumption rather than a direct consequence of <mass conservation>.
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