An Approximation of the Improved Rouse Equation

Abstract

Rouse equation, which was derived from the diffusion theory, is well known in the study of steady state suspended sediment transport over erodible beds. Although this equation being regarded as Rouse law could be applied effectively, it is unrealistic that the concentration at the free surface is always zero. In addition, for deriving the depth-averaged concentration, the numerical integration or the table lookup has to be performed. Bose and Dey[1] improved the Rouse equation using a modified sediment diffusivity in order to overcome the zero value concentration, but this equation can not be integrated analytically yet. In this paper, according to two equilibrium profiles respect to constant and linear diffusion coefficients, an approximate solution of the improved Rouse equation is given using a general weight-averaged method in order to be integrated analytically. Through verification with experimental data, the results show that the approximation of the improved Rouse equation behave generally better than itself, as well as the Rouse equation and van Rijn equation over the whole water depth. It is revealed that, nevertheless some empirical, this approximation is reasonable, and has higher accuracy. Moreover it can be integrated analytically.