= Axisymmetric settling box model
{title2=$\pi R^2h=\mathcal V,\quad\dot c=-w_sc/h$}
An axisymmetric <gravity-current box model> with no entrainment and negligible suspended-particle volume loss has constant bulk volume $\mathcal V$, uniform height $h$, and uniform particle volume fraction $c$. For an absorbing horizontal bed and downward <settling velocity> $w_s>0$, particle <mass conservation> gives $\dot c=-w_sc/h$. A constant front <Froude number> closes spreading by $\dot R=\operatorname{Fr}\sqrt{g_0ch}$, where $g_0=g(\rho_p-\rho_a)/\rho_a$ is buoyancy per unit volume fraction. This model describes the mixed bulk and its head closure, not the initial inertial blast or a resolved head shape.
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