Abstract
The principle of dynamic entrainment is applied to the turbulent-mixing problem. With use of the velocity fluctuations characteristic of turbulent flow and the equation of continuity, an expression is derived for the mass exchange between an accelerated fluid and its environment, under steady-state conditions. A two-stage diffusion mechanism is postulated, in which it is held that the dilution and spreading of aerosols occur in consequence of the inflow and outflow required by continuity in regions of accelerated motion. It is assumed that the inflow and outflow are orderly, that the atmosphere is incompressible, that changes in density are negligible, and that the entrained air is uniformly mixed with the aerosol. Several elementary models are described, and the results obtained by numerical integration in selected cases are discussed. It is indicated that the turbulent-mixing process depends upon the scale of the velocity fluctuations, and upon the ratio of the amplitude of these fluctuations to the mean wind speed.
