Diffusion layer thickness in turbulent flow

Abstract

Average thickness of diffusive layers in a turbulent flow is described using an idea of Lagrangian meso-scale element convected by mean flow and large scale turbulence. This idea enables a formulation of a simple model for the diffusive layer thickness assuming that its evolution is determined by the diffusive growth and two components, compressive normal and tangential, of the turbulent strain rate tensor. Analysis of the possible effects of the folding action of the turbulence leads to the conclusion that the folding becomes significant only at the scales far superior to the considered dimensions of the meso-scale elements, thus it may be neglected in the present formulation. The evolution equation for the meso-scale element thickness is derived and put to test against experiments conducted in plane and round jets. The model proved capable of producing, using the same values of two model constants, values of the diffusive layer thickness in good qualitative agreement with the measurements.While the present numerical simulations of the turbulent jets are made using very simple, perhaps simplistic, flow and turbulence description, they nonetheless allow a fairly accurate estimation of turbulence microscales at different locations in a jet. It turns out that neither Kolmogorov nor Taylor scale provides a good universal reference scale for the diffusive layer thickness and it is local turbulence conditions and history of the meso-scale element determining the latter.