 Triangular-channel dry-bed dam break

In a prismatic triangular channel with wetted area proportional to $h^2$, the Riemann invariants are $u\pm 4c$, with $c^2=gh/2$. Releasing water initially at rest into a dry channel produces a rarefaction wave with $u+4c=4c_0$ and $x/t=u-c$. Hence $c=(4c_0-x/t)/5$, $u=4(c_0+x/t)/5$ and the displayed depth profile for $-c_{0}t<x<4c_{0}t$. The dry front advances at $4c_0$ before finite-reservoir or varying-channel effects become important.