= Fixed-energy two-layer entrainment law
{title2=$h/h_0=(1+A\Omega t)^{2/5}$}
For <potential energy of two-layer entrainment> with constant $B=g'h$, the <fixed-energy turbulent mixed layer> assumption gives $u_U^2h=C_K^2\Omega^2R^2h_0$. If $u_I=C_Iu_U$ and the <interfacial power model for entrainment> applies with fixed coefficients, integration gives the displayed depth law with $A=5C_Wc_DC_I^3C_K^3\Omega^2R^3/(Bh_0)$. The relation applies only before the layer reaches the tank bottom. Its <interfacial Richardson number> $Bd_I/(h u_I^2)$ stays constant for fixed interface thickness, whereas it decreases like $h^{-1}$ in the constant-speed entrainment model.
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