A new theory of turbulent diffusion is developed so as to describe the dynamics of particulate matter in fluid suspensions. In order that the statistical description be consistent with force equation dynamics of sedimentation, a new diffusion equation is derived from the postulates of a past‐future stochastic process.A steady‐state suspension of particles in a turbulent stream is treated like an atomosphere. Dimensional arguments are used to retain the most relevant physical entities in a linear theory. It is shown that the bed load and mid‐stream suspension of a muddy stream cannot be considered separately. Some experiments are discussed in this connection. A qualitative theory of sand rippling is explained in terms of the instability of a flat sandy bottom under certain turbulence conditions. A singular perturbation method is employed to obtain an asymptotic expansion of the solution of the equilibrium equation.Assumptions are discussed and criticized. The advantage of the theory is that all statistical coefficients are averages of familiar dynamical quantities.