Deposition of Cohesive Sediment from Turbulent Plumes, Gravity Currents, and Turbidity Currents

Models for the deposition of cohesive sediment from turbulent plumes (or “buoyant jets”), gravity currents, and turbidity currents are provided in this paper. The cohesive sediment is made up of small particles that aggregate together to form larger flocs, which are in turn broken up by turbulent shear. The equilibrium mean floc size (and thus the equilibrium mean fall speed) is a function of the turbulent dissipation rate and the sediment concentration. The flows are modeled by using integral and box models, with dissipation related to bulk flow properties. For plumes it is shown that there is a well-defined equilibrium fall speed at the virtual origin and that the fall speed changes relatively slowly in the momentum-dominated part of the flow (within one jet length or so of the source). If the flocs are assumed to adjust instantaneously to their equilibrium size, an integral model for a turbulent plume carrying cohesive sediment can be described in terms of two parameters: the angle between the plume and the horizontal at the virtual origin and the (nondimensional) fall speed there. Next, a typical time scale for flocs to adjust to their equilibrium size is identified, and the model is extended to include an equation for the rate of change of the mean floc size along the plume. The time scale over which the mean floc size changes can be compared with a natural time scale for the plume (the time taken for a particle traveling at the mean plume speed to travel a jet length). Thus, in this nonequilibrium model, a further nondimensional parameter is identified, $B$, which is proportional to the ratio of a typical plume time scale to the typical floc size adjustment time scale. When $B$ is large, the flocs adjust almost instantaneously to the equilibrium size, whereas when $B$ is very small, the flocs remain close to their size at the source. However, whatever the value of $B$ (which is in terms of typical time scales), the local adjustment time scale always tends to zero approaching an idealized source (virtual origin) so that the equilibrium model is always valid there. For plumes injected horizontally, the equilibrium floc size tends to reduce with distance from the source, with any reduction in turbulent shear more than compensated for by the reduction in sediment concentration. The equilibrium model is then applied to two-dimensional and axisymmetric gravity currents and turbidity currents. The gravity currents are assumed to be steady flows driven by a constant source of dense fluid with the sediment having a negligible effect on the fluid density. In contrast, the turbidity currents modeled are initiated by the release of a finite volume of fluid containing the sediment, with the sediment concentration providing the density difference from the ambient fluid. For these flows, the basic scales are identified, and the concentration and deposition distributions given.