Cómputo de la incorporación de sedimento en suspensioón en flujos turbulentos no permanentes utilizando un enfoque estocástico

In order to compute the total amount and vertical distribution of suspended sediment, a reference concentration near the bed or entrainment function is needed, and considerable research effort has been dedicated to obtain such formulae. Several entrainment functions are available in the literature, but all of them have been developed for steady, uniform flow conditions. The ability of such relationships to predict entrainment rates in unsteady flows has not been demonstrated, nor has there been any attempt to develop a general formulation that works for both steady and unsteady flow conditions. The traditional approach relates the entrainment of sediment to the wall shear stress associated with skin friction in a deterministic way, providing only a relation between mean values. An alternative is to consider both the shear stress and the entrainment as stochastic turbulent quantities and to express them in terms of their probability density functions (PDFs). In this way, statistics of the entrainment can be obtained from measured shear stress PDFs, either in steady or unsteady situations, since the effect of unsteadiness is embedded in the PDF. This new methodology was used to estimate sediment entrainment produced by the passage of vessels in the Mississippi River and the Illinois River. Using a low order cumulant expansion to describe the PDF of the shear stress and a generalized version of García and Parker's entrainment relationship, an expression for the average of the entrainment as a function of the average, variance, skewness and flatness of the shear stress distribution was obtained. Predictions compared favorably with values reported in the literature.