= Constant-flux river momentum relaxation
{title2=$u_t+[Q/(F^2u^2)-u]u_X=(1-u^3/Q)/(\varepsilon F^2)$}
This scalar <quasilinear partial differential equation> results by imposing $h=Q/u$ in a frictional river momentum equation and measuring $X$ upstream. It retains a relaxation toward $u_0=Q^{1/3}$ and carries information at speed $c(u)=Q/(F^2u^2)-u$. Near equilibrium the relaxation time is $\varepsilon F^2u_0/3$. A slowly moving downstream boundary can generate an attached <boundary layer> when $c(u)$ exceeds its speed throughout the relaxation. The model retains momentum dynamics only: exactly constant flux in both original <Saint-Venant equations> would instead force time-independent depth.
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