= Variable-width shallow-water characteristics
{title2=$D_\pm(u\pm2c)=\mp cu\,b'/b$}
For a rectangular channel with stationary width $b(x)$ and constant <reduced gravity> $g'$, <volume conservation> and <momentum conservation> give $h_t+uh_x+hu_x=-hu b'/b$ and $u_t+uu_x+g'h_x=0$. With $c=\sqrt{g'h}$ the <characteristic curves> have speeds $u\pm c$. The combinations $u\pm2c$ obey the displayed compatibility equations; they are <Riemann invariants> only when the width source term vanishes.
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