Distribution of suspended sediment concentration in wide sediment-laden streams: A novel power-law theory

The diffusion equationof suspended sediment concentration in a wide sediment-laden stream flow is dependent on the vertical gradient of streamwise velocity and the sediment diffusivity. This study aims at investigating the influence of the streamwise velocity laws on the suspended sediment concentration distributions, resulting from the solution of the diffusion equation. Firstly, the sediment concentration distributions are obtained numerically from the solution of the diffusion equationusing different velocity laws and compared with the experimental data. It is found that the power-law approximation produces good computational results for the concentration distributions. The accuracy of using a power-law velocity model is comparable with the results obtained from other classical velocity laws, namely log-law, log wake-law and stratified log-law. Secondly, a novel analytical solution is proposed for the determination of sediment concentration distribution, where a power-law, wall-concentration profile is coupled with a concentration wake function. The power-law model (for velocity and concentration) is calibrated using the experimental data, and then a generalized wake function is obtained by choosing a suitable law. The developed power-law model involving the wake function adjusted by an exponent predicts the sediment concentration distributions quite satisfactorily. Finally, a new explicit formula for the suspended-load transport rate is derived from the proposed theory, where numerical computation of integrals, as needed in the Einstein theory, is avoided.