A Simple Floc-Growth Function for Natural Flocs in Estuaries
Natural flocs in an estuary grow with increasing time, salinity, suspended particulate matter concentration, and with decreasing turbulence. Although various theoretical and empirical functions for floc growth have been proposed in the literature, they are all complex. It is argued in this study that there should be a simple and general function of floc size D against time t, salinity S, suspended particulate matter concentration C, microscale η, and biochemical composition M. Theory and experiments seem to corroborate that average floc size responds systematically to its drivers. Moreover, the response is partly similar to all drivers: a lower plateau followed by a rise, and partly different: an upper plateau for t, S and a fall for C, η. Assuming drivers are independent, each curve is normalized around its rise. The drivers are joined into one variable X that holds each normalized driver with equal weight. The result is a function that gives floc size against this composite variable X. This composite variable in turn is a function of ambient conditions and the function predicts floc size for any set of ambient conditions. The case is presented here using linear segments, but eventually the logistic growth function is proposed. © 2011 International Association for Mathematical Geosciences.