The turbulent diffusion of a passive scalar quantity

Consideration is given to the dispersion of a passive contaminant in a turbulent flow. An equation relating the turbulent diffusion flux in the absence of molecular diffusion to the velocity distribution is obtained from the instantaneous turbulent transport equation, and the closure of the equation by a gradient law and a law of the second order in mean concentration is examined for the case of homogeneous turbulence. It is shown that the gradient law requires a Gaussian velocity field, while the more general second-order law is capable of taking into account velocity asymmetries.