Parameterized expressions for an improved Rouse equation

The equilibrium profile of suspended sediment concentration (SSC) in steady, uniform turbulent flow has been extensively studied since the proposition of Rouse equation (Rouse, 1937). Many researchers keep studying and attempting to improve the Rouse equation by modifying the mixing length concept. Bose and Dey (2009) improved Rouse equation based on the modified sediment diffusivity, however, their proposed sediment diffusivity has two parameters, the depth modification factor αand the reciprocal of the sediment Schmidt number β = 1Sc, and the corresponding expressions were not given properly in their paper. This paper aims to parameterize the relevant coefficients, the results shows: (1)α is parameterized from a reasonable approximation by the analysis of surface boundary condition of SSC; (2) considering some effect factors on the settling velocity, β can be expressed by an extended and modified Montes-Ippen formula, and its related parameters are calibrated by substantial data about the relationship between the primary Rouse parameter Z* = ωs/κu* and its counterpart Z'* = ωs/βκu*. Through verification with some experimental and field datasets, and comparison with related formula, the results show that the sediment diffusivity and SSC profiles have a good agreement with measured data used the present parameterized expressions of α and β, so the present improved Rouse equation is reasonable, and can be applied in practical applications. Finally, an approximation and simplified expression of the improved Rouse equation is deduced by using the approach of perturbation, which can be applied easily for the estimation of suspended sediment transport rate.