A heuristic formula for turbulence-induced flocculation of cohesive sediment

This paper presents new measurements on the settling velocity of mud flocs in the Lower Sea Scheldt, Belgium, and compares the results with data obtained previously in the Tamar estuary, UK. The data show that the flocs are fairly compact with a fractal dimension of about 2.2, which is indicative for reaction limited aggregation processes, characteristic in dynamic aquatic systems with large tidal flow velocities and high SPM (suspended particulate matter) concentrations. The data also reveal a fairly small dependency of the settling velocity from SPM concentrations, consistently much smaller than earlier data published in literature. Furthermore, a simple explicit formulation is proposed for the settling velocity of cohesive sediment in estuaries and coastal seas. It is derived from an analytical solution of a Lagrangean flocculation model, which accounts for turbulence-induced aggregation and floc break-up. Also the effects of variations in SPM and of a limited residence time of the flocs in the turbulent water column are included. The model has been calibrated against data from settling velocity measurements carried out in the Tamar estuary. Values of the measured settling velocity vary between 0.5 and 5 mm s−1 at SPM-values between 0.05 and 8 g l−1. Using the tuned coefficients, the model describes the observations satisfactory, with an overall relative standard deviation of 30%. Also, the well-known and observed increase in settling velocity with turbulent shear stress at low stresses and the opposite trend at high stresses is described properly. Next, the model is applied to the new data obtained in the Lower Sea Scheldt estuary, again comparing favourably with overall relative standard deviations of 30–50%. It appeared that the coefficients of the model can be determined from independent measurements, but two of them have to be determined by trial and error, for which a simple procedure is proposed.