Derivations of distributions of diffusivity, flow velocity, and sediment concentration over the flow depth were made for a generalized normalization of the relative distance from the flow boundary. Boundary condition restraints suggest a normalization function with a finite lower limit and an infinite upper limit. In analytical considerations, the distribution functions were discussed relative to an unspecified mean turbulent diffusivity. An analysis of the distributions was made in terms of their limits at the channel boundary and the free surface (or top of the boundary layer).