Numerical Results for Vertical 2-D Sediment Diffusion Equation and Approximate Vertical Distribution of Concentration in Non-equilibrium Condition

This chapter presents the numerical results for the vertically 2-D sediment diffusion equation. In the past the bottom boundary conditions used in these studies were not consistent with the reality. The main contents of Chapter 8 consist of: (1) The bottom boundary condition based on the sediment exchange intensity on the bed, is adopted for the vertically 2-D diffusion equation. This boundary condition has solid theoretical basis, with parameters being widely used and verified in the 1-D equation for non-equilibrium sediment transport. (2) The parameters in the bottom boundary condition, such as the suspension height and the saturation recovery coefficient, depend on the vertical distribution of sediment concentration and the saturation condition. In other words, this bottom boundary condition is coupled with the diffusion equation. Hence, the numerical solution of the diffusion equation is solved in a coupled manner. (3) A series of numerical solutions are computed. Analyses show that these numerical solutions are reasonable, and can represent the vertical distribution of sediment concentration and its longitudinal variation along the flow path for the case of scour or deposition. (4) For non-equilibrium sediment transport, the distribution of sediment concentration in vertical direction is quite complicate. Introducing the un-saturation factor C, and considering the variation of the bottom sediment concentration, a simplified formulation is derived to approximate the vertical distribution of sediment concentration under the non-equilibrium condition, which shows good agreement with the numerical solutions for most cases except for the saturation coefficient \({S}/{S}^{*} > 5\) .