Prismatic triangular-channel gravity-current box model
= Prismatic triangular-channel gravity-current box model
A uniform-depth <particle-laden gravity current> in fixed triangular cross section has conserved <volume> proportional to $h^2X$. A <gravity-current front condition> and absorbing-boundary <particle deposition flux> give $\dot X=\operatorname{Fr}\sqrt{G\phi h}$ and $\dot\phi=-2w(\phi)\phi/h$. The box describes late-time bulk evolution; it does not resolve the nose or immediate dam-break flow.