Diffusion Equation and Boundary Conditions for Non-uniform Suspended Load

Focusing on the convection-diffusion equations for non-uniform suspended load and the bottom boundary condition, the contents of this chapter are summarized as follows: (1) The convection-diffusion equation for uniform suspended load is extended to non-uniform sediment, and the size distribution of suspended load is defined. (2) The 3-D convection-diffusion equation for non-uniform sediment is integrated over the channel width and over the water depth, respectively, under certain conditions to derive the horizontally and vertically two-dimensional (2-D) equations, respectively. (3) Based on the statistical theory for the sediment exchange on the bed, the bottom boundary condition for the convection-diffusion equation is developed. (4) Integrating the 2-D convection-diffusion equation over the water depth and using the boundary condition obtain 1-D sediment transport equation. (5) The water volume percentage is introduced for the case of strong equilibrium transport, which is the important parameters for expressing the carrying-sediment capacity and will be extended to the case for non-equilibrium transport.