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Fine-Sediment Deposition from Gravity Surges on Uniform Slopes
W. Brian Dade, John R. Lister, Herbert E. Huppert
The propagation of and the deposition from a noneroding, turbulent gravity surge are described by a simple model for a two-dimensional, well-mixed buoyant cloud of suspended particles moving down an inclined surface. The model includes the effects of entrainment of ambient seawater, deposition of suspended sediment, seafloor friction, and slope. Our results are applicable to large, decelerating turbidity currents and their distal deposits on uniform slopes in lakes and the sea. The scaling arguments that emerge from our analysis, moreover, have important ramifications for the design and interpretation of laboratory analogs of these phenomena.
General solutions are obtained to the coupled equations that describe the evolution of momentum, total mass, and particulate mass of a surge. The solutions vary on two horizontal length scales: xo, beyond which the behavior of the surge is independent of the initial momentum and shape; and xr, beyond which the driving negative buoyancy of the surge is lost due to particle settling. For fine particles whose settling velocity is much less than the forward propagation speed of the surge, the suspension is well mixed and xo << xr, The deposit thickness diminishes as the inverse square root of the downstream distance x when xo << x << xr, and then diminishes exponentially with downstream distance as x approaches and exceeds xr.
The length of a surge deposit scales with xr = kbosin/aws(cos)2, where k is the assumed constant aspect ratio of the surge, bo is the initial buoyancy per unit width at the point of issue onto a slope of constant angle ,a is the ambient density, ws is the average settling velocity of the suspended particles, and = 6 + 8CD/ incorporates the ratio of the constant coefficients of drag CD and fluid entrainment .
Extension of our model to the case of two particle sizes indicates that, even for very poorly sorted suspensions, the estimate for the length of a surge deposit xr is valid if ws is defined as the volume-averaged settling velocity of the initial suspension at xo. The ratio of coarse to fine material in model deposits generated from initially poorly sorted suspensions can diminish dramatically in the downstream direction, however, due to differential rates of gravitational settling.
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