Significance of probabilistic parameterization in cohesive sediment bed exchange

The primary issue addressed in this study is whether the decades old paradigm of exclusive erosion or deposition in turbulent flow has legitimacy based on physical principles within cohesive sediment dynamics. The exclusive paradigm assumes that sediment exchange condition at the bed-water interface is either erosion, deposition or neither, but never both. In contrast, the more recently espoused simultaneous exchange paradigm admits the possibility of erosion and deposition of cohesive sediment occurring at the same time.The exclusive paradigm is, in part, the result of early attempts to understand basic cohesive sediment transport behavior based on inferred data in laboratory apparatuses such as flumes averaged over time and space. The time scale of averaging is longer than the time scale of turbulence and the spatial dimension is scaled by water depth in the apparatus. Bed sediment exchange has been deduced primarily from the increase or reduction in the suspended sediment concentration within the water column, rather then from difficult to record observations of particle movement very close to the bed surface. The net result of averaging will be positive, negative or zero sediment flux at the bed surface, but not both positive and negative.With the inclusion of greater details in newer mathematical models, such as particle size distributions and flocculation sub-models, the bed exchange algorithms have required revision. Numerical modelers have found the need to use the simultaneous approach to replicate observed sedimentation rates in the field environment.The numerical sediment transport tool developed for this research has been shown to be capable of simulating several processes critical for simulation of bed exchange. These processes include aggregation and disaggregation dynamics, stochastic effects in bed exchange and aggregation/disaggregation, hindered settling, attainment of a depositional or erosional equilibrium concentration for a fixed shear stress, and floc spectrum features documented by field experimentation.Observations made during development and application of the numerical tool are: (1) The effects of a probabilistic treatment of the key variables are more pronounced for erosion than for deposition. These variables include current velocity, bottom shear stress, floc shear strength, critical shear stresses for erosion and deposition, internal shear and settling velocity. (2) Probabilistic effects are amplified through the flocculation model over the effects that occur through bed exchange alone. (3) For a given shear stress the flocculation model will tend toward an equilibrium distribution of particle sizes. (4) The probabilistic treatment results in a broader floc distribution spectrum than occurs with use of mean-valued variables. (5) Deposition or erosion will be initiated sooner and transition from one to the other more gradual in response to changing shear stress when a probabilistic treatment is used compared to a mean-valued treatment. The differential timing will be a function of the standard deviations of the probabilistic variables and the rate of change of the shear stress. (6) The use of the exclusive paradigm with a floc size distribution can perform as well as a simultaneous treatment with a single particle size. (7) A simulation was performed of a flume test by Parchure and Mehta (1985) designed to evaluate the exclusive versus simultaneous paradigm by diluting the concentration of a flume suspension that had achieved an equilibrium concentration from bed erosion. If the 37 exclusive paradigm was valid, the concentration at the end of dilution should remain constant. If the concentration began to rise after dilution was ceased, then the simultaneous paradigm would be an explanation. The flume concentration did rise after the dilution stopped, but at a very low rate of erosion. The numerical model was able to replicate the flume behavior with the correct rate of rise after the end of dilution by using the exclusive paradigm with a probabilistic treatment of the variables. (8) The appropriate use of either the exclusive or continuous paradigm appears to be dictated by the level of temporal and spatial averaging used in the development of empirical data and in the formulation of the variables in the analysis.Empirical coefficients developed for mean-valued analysis may require adjustment when used in a probabilistic treatment.