= Entrainment exponent from a local interfacial Richardson closure
{title2=$E\propto\mathrm{Ri}_i^{-3/2}$}
Combine a fixed-energy mixed-layer relation $u^2h=A\Omega^2R^3$, jump $g'=N^2h/2$, and stress power proportional to $u^3$ with an energy-transfer factor $(\Omega/N)^\alpha(\delta/R)^\beta$. Eliminating depth in favor of the <interfacial Richardson number> gives $E\propto(\Omega/N)^{\alpha-1}(\delta/R)^{\beta+3/2}\mathrm{Ri}_i^{-3/2}$. A local-only <entrainment> closure requires $\alpha=1$, $\beta=-3/2$ and exponent $3/2$ on the <Richardson number>.
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