= Sedimenting triangular-channel characteristic compatibility
{title2=$dx/dt=u,\ u\pm c$}
For the <prismatic triangular-channel shallow water equations>, $c^2=G\phi h/2$. The <characteristic speeds> are $u,u\pm c$. Along $dx/dt=u$, $d\phi/dt=-2w\phi/h$. Along $dx/dt=u\pm c$, the <hyperbolic system> has compatibility relation
$$
du\pm4\,dc\mp\frac{4c}{3\phi}\,d\phi=\mp\frac{4wc}{3h}\,dt.
$$
The <concentration> differential cannot generally be discarded to obtain <Riemann invariants> $u\pm4c$. Positive depth and <concentration> are required for this nondegenerate form.
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