On equilibrium profiles of suspended particles

A power law is often used to represent the vertical profile of uniform suspended particles above a horizontally homogeneous surface. It serves as an analytical solution representing an equilibrium between vertical turbulent diffusion and gravitational settling, andcan be used to extract settling velocity information from observed particle number density profiles. In this note, we analyse this situation and use a numerical model to investigate the temporal change of particle number density and of the net vertical flux due to turbulent diffusion and gravitational settling. The results show that the net flux approaches zero very slowly for small particles (w_s/ u_* < 1), and show that the power law does not hold for small particles. If the power law is used to extract settling velocities from observed vertical distributions of particle number density in these cases, the estimated settling velocity may be unrealistically large.