Abstract: In this article, we treat the problem of two-dimensional uniform steady channel flow of turbid water with theory of similarity. Under the condition of similarity of turbulent fluctuation velocity and fluctuation of concentration of sand particles, we obtain the profile of the vertical distribution of concentration of sand particles. This profile of vertical distribution of concentration of sand particles is slightly different from that obtained by diffusion theory, and departs from that obtained by gravitational theory.

Key words: singular perturbation, reaction diffusion equation, initial boundary value problem