Mean velocity and suspended sediment concentration profile model of turbulent shear flow with probability density function

Abstract

This work purposes a general mean velocity and a suspended sediment concentration (SSC) model to express distribution at every point of the cross section of turbulent shear flow by using a probability density function method. The probability density function method was used to describe the velocity and concentration profiles interacted on directly by fluid particles in the turbulent shear flow to solve turbulent flow and avoid different dynamical mechanics. The velocity profile model was obtained by solving for the profile integral with the product of the laminar velocity and probability density, through adopting an exponential probability density function to express probability distribution of velocity alteration of a fluid particle in turbulent shear flow. An SSC profile model was also created following a method similar to the above and based on the Schmidt diffusion equation. Different velocity and SSC profiles were created while changing the parameters of the models. The models were verified by comparing the calculated results with traditional models. It was shown that the probability density function model was superior to log-law in predicting stream-wise velocity profiles in coastal currents, and the probability density function SSC profile model was superior to the Rouse equation for predicting average SSC profiles in rivers and estuaries. Outlooks for precision investigation are stated at the end of this article.