Influence of the sampling time on the kinematics of turbulent diffusion from a continuous source

Abstract

A kinematic description is presented of how turbulent diffusion from a continuous source varies with the sampling time in stationary, homogeneous turbulence. Unlike most previous theories, the sampling is assumed to take place at fixed downstream distances from the source. It is shown that the sampling-time effects depend on two-particle velocity statistics. Thus, time-average diffusion at fixed downstream distances is more akin to relative diffusion than to absolute diffusion. Two simple diffusion models are developed from the kinematic equations. These models are in fairly good agreement with diffusion data obtained both in a wind tunnel and in the field. Moreover, these models have significant practical implications. For example, the models indicate that care must be taken when using band-pass spectral filtering as a paradigm for turbulent diffusion. Also, the models show that the mean flow speed U has an important influence on the sampling-time effects. To account for U properly, diffusion measurements with differing sampling times Λ should be compared using the product UΛ, and not just Λ.