= Rotating-disc mixed-layer depth law
{title2=$h/R\propto[\Omega^2R/(N^2\delta)]^{1/3}(\Omega t)^{2/9}$}
With constant interface thickness and the local <entrainment> exponent $3/2$, the <fixed-energy turbulent mixed layer> satisfies $\dot h=C\Omega^4R^6/(N^3\delta^{3/2}h^{7/2})$. Integration gives a linear growth law for $h^{9/2}$. Once an initial-depth offset is negligible, $h/R$ scales as $[\Omega^2R/(N^2\delta)]^{1/3}(\Omega t)^{2/9}$. The law applies before the mixed layer reaches the tank bottom and after the initial forcing transient.
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