Einstein Bed-Load Function at High Sediment Rates

In alluvial channels consisting of fine sand beds, almost all the sediment load moves in suspension with high concentrations near the bed. These high concentrations affect many of the flow characteristics: the roughness is changed, the velocity profiles are altered, the density and viscosity of the fluid are increased, and the particle fall velocity and the von Karman coefficient are reduced. The paper describes how the Einstein bed-load function can be modified in order to better describe flows with high sediment rates of fine grain. Instead of a constant value of von Karman's coefficient of 0.4, both the distributions of velocity and suspended sediment use a variable value of von Karman's coefficient which is a function of a dimensionless parameter but becomes 0.4 when the parameter is larger than 1.