= Front-regularized triangular-channel dam break
{title2=$c_f=4c_0/(4+\sqrt2F),\quad u_f=\sqrt2F c_f$}
In a prismatic triangular channel with constant <reduced gravity>, the wave speed is $c=\sqrt{g'h/2}$ and the <Riemann invariants> are $u\pm4c$. A dam release into a deep ambient produces a simple-wave rarefaction with $u+4c=4c_0$. The imposed <gravity-current front condition> $u_f=F\sqrt{g'h_f}$ gives the displayed uniform nose-adjacent state. The fan has $c=(4c_0-x/t)/5$ and $u=4(c_0+x/t)/5$, extending from $x/t=-c_0$ to $u_f-c_f$; a uniform region then reaches the front $x/t=u_f$. The nose closure supplies physics absent from the one-layer interior equations.
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