Turbulent diffusion in a medium subjected to uniform deformation

Abstract

Turbulent diffusion in media subjected to uniform deformation caused by the presence of average-velocity gradients which are constant throughout the space is an idealization of real processes, in particular, of processes such as diffusion in channels of variable cross-sectional area [1], in the lowest layers of the atmosphere [2], etc. In this article we formulate the problem of the connection between the statistical characteristics of the transfer of a passive substance in turbulent diffusion in deformed media with the statistical characteristics of the turbulence. The statistical transfer characteristics generally used are the first two moments of the vector of random displacement of a liquid particle under the action of turbulent pulsations in velocity: the average displacement and the components of the dispersion tensor of the displacement of a liquid particle. We obtain connecting relations for the dispersion tensor of a liquid particle in turbulent diffusion of a passive substance in a uniform turbulent medium subjected to uniform deformation caused by average-velocity gradients which are constant throughout the space. These relations are a generalization of known expressions for undeformed media [2, 3]. We investigate the case of rapid deformation when the turbulent characteristics of the medium vary in accordance with the linear theory [4].