Estimating Bed-Load Advection And Dispersion Coefficients With The Method Of Moments

The Advection Dispersion (AD) equation is commonly used to simulate solute, wash load, and even suspended load transport, but is rarely applied to bed load. The obstacle to applying AD equation to bed load transport is empirical; it is challenging to estimate the advection and diffusion coefficients. This paper applies the method of moments to a flume experiment to compute the AD bed load coefficients. Five colors of otherwise identical sand were introduced into an equilibrium sediment flume in sequence. After the experiment, surface, bed samples were collected along the length of the flume and sieved into eight-grain classes. Color distributions of each sample and each grain class were computed with image analysis. Longitudinal Probability Mass Function (PMF) of each color and each grain class were computed from these data. The method of moments was applied to the PMF of the particle displacements, where the advection coefficient was the temporal derivative of the first moment of each color and, the diffusion coefficient was defined as the temporal derivative of the variance. In this paper, advection and dispersion coefficients are computed for coarse sand material that consists of mean diameter of 1.3mm