= Finite-Froude lock-release rarefaction
{title2=$h_f/H=4/(F+2)^2$}
A semi-infinite resting layer of depth $H$ and constant <reduced gravity> $b$ released into a deep ambient develops a <rarefaction wave> satisfying $u+2\sqrt{bh}=2\sqrt{bH}$. The head closure $u_f=F\sqrt{bh_f}$ gives $h_f=4H/(F+2)^2$ and $u_f=2F\sqrt{bH}/(F+2)$. A constant-depth shelf lies between the rarefaction tail speed $u_f-\sqrt{bh_f}$ and the front speed $u_f$; its width is positive for every finite positive $F$.
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