Finite-volume triangular-channel current
= Finite-volume triangular-channel current
{title2=$L^{5/4}=L_0^{5/4}+(5/4)F\sqrt{g'}(2V_0)^{1/4}t$}
A <gravity-current box model> in a prismatic channel with width equal to height has volume $V_0=Lh^2/2$. Closing the front speed by $\dot L=F\sqrt{g'h}$ gives the displayed law and long-time spreading $L\propto t^{4/5}$. This is an integral approximation with constant volume and <reduced gravity>, not an exact uniform-depth solution of the local <shallow water equations>.