A box model for non‐entraining, suspension‐driven gravity surges on horizontal surfaces

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Abstract
The propagation of and the deposition from a turbulent gravity current generated by the release of a finite volume of a dense particle suspension is described by a box model. The approximate model consists of a set of simple equations, a predetermined, depth‐dependent leading boundary condition and one experimentally determined parameter describing the trailing boundary condition. It yields predictions that agree well with existing laboratory observations and more complex theoretical models of non‐eroding, non‐entraining, suspension‐driven flows on horizontal surfaces.The essential features of gravity‐surge behaviour have been observed and are captured accurately by the box model. These include the increased rate of downstream loss of flow momentum with increased particle setting velocity, the existence of maxima in the thickness of proximal deposits, and the downstream thinning of distal deposits. Our approximation for the final run‐out distance, xr, of a surge in deep water is given by xr3(g'oq3o/w2s)1/5, where g'o is the initial reduced gravity of the surge, qo the initial two‐dimensional volume, and ws the average settling velocity of the particles in the suspension. A characteristic thickness of the resulting deposit is given by φoqo/xr'where øo is the initial volumetric fraction of sediment suspended in the surge.Our analysis provides additional insight into other features of gravity‐surge dynamics and deposits, including the potential for the thickening of currents with time, the maintenance of inertial conditions and the potential for strong feedback in the sorting of particle sizes in the downstream direction at travel distances approaching xr. Box‐model approximations for the evolution of gravity surges thus provide a useful starting point for analyses of some naturally occurring turbidity surges and their deposits.

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