Sediment Dispersion in Flow with Moving Boundaries

The longitudinal dispersion equation for sediment in unsteady nonuniform flow with moving boundaries is formulated from the three-dimensional instantaneous diffusion equation for movement of sediment by means of the time- and space-averaging processes. The equation is then studied for its applicability and validity in the sediment problem. The analytical expressions of the longitudinal dispersion coefficient for sediment in flow with moving boundaries are obtained for both turbulent and laminar flow. The effect of moving boundaries in turbulent flow on the value of the longitudinal dispersion coefficient has theoretically been shown to be negligible, but may be significant at a place where a sand or water wave breaks, causing an infinite gradient of bed or flow profile. The longitudinal dispersion equation that may often be called the suspended-load equation is shown to play an important role in the mathematical modeling of an alluvial channel where the suspended bed-material discharge is greater than the contact-bed discharge.