Statistical Model of Turbulence in Sediment-Laden Streams

Turbulent flow in a sediment laden stream is described by a random walk model which simulates the behavior of sediment particles, fluctuating in depth near the surface of the stream down to the stream bed. The basic aspect of this model is the probability laws which govern the transfer of mass for both water and sediment from one level to another throughout the total depth. The downstream velocity at each level is introduced to convert mass to momentum. Three sources of momentum loss are taken into account. The downstream velocities at the various levels, which are unknown, are determined from a set of equations based on the assumption that the expected momentum at a given level equals the sum of the expected momentum contributed at time Δt previous from all levels and by gravity. The solution of these equations in the limit where the distance between levels goes to zero leads to the vertical velocity distribution of the sediment-water mixture which is dependent upon four parameters.