Analysis of Fine-Grained Sediment Movement in Small Canals

Abstract

A one-dimensional mathematical model is presented for quantification of fine-grained sediment movement in small canals. The model is based on the time-dependent, advection-dispersion equation. The model simulates the effects of deposition and erosion through appropriate sink and source terms. The rate of deposition is treated by a linear relation, and the rate of erosion is represented by an exponential function. Selective settling and consolidation effects are incorporated through the depositional and erosional terms. The governing equation is solved by a finite integral transformation that reduces the original PDE into a Sturm-Liouville ODE. Closed-form solutions are given in terms of eigenseries for various boundary and initial conditions. Depending on the situation, the eigenfunctions and eigenvalues are obtained either analytically or estimated by using the Kramers-Wentzel-Brillouin (KWB) approximation. Comparison of the simulated results with experimental data has shown good agreement.