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We summarize the physical equations and analytic solutions of three versionsof the box model equations, suitable for the integral formulation ofaxisymmetric gravity-driven particle currents with constant volume. The firstmodel is based on a simple constant resisting stress, while the second andthird models assume flow dilution by particle deposition. The third model ischaracterized by assuming an interstitial fluid lighter than the ambient fluid.All the calculations are performed on a flat topography. Ambient fluidentrainment and cooling effects are not considered. All particles are assumedto deposit at the same velocity.

Notes on the analytic solution of box model equations for gravity-driven particle currents with constant volume