Diffusion of Clouds of Contaminant in a Turbulent Boundary Layer

Abstract

Under the assumption that the detailed turbulence structure in the constant-stress region of a fluid flowing over a rough wall is in a universal state determined wholly by the friction velocity u* a similarity analysis of a Lagrangian type can be applied to the relative dispersion of clouds of contaminant released in such a layer. It is found that for the case in which the initial dimension of the cloud, say L, and the initial mean height are comparable, there are only two temporal regimes and they are characterized by times smaller than or greater than L/u*. For the small time regime all relative diffusivities are linearly dependent on time and their directional properties are related to Eulerian measurements. Of more interest are the predictions in the long time regime. It is also found in this region that relative diffusion is characterized by a diffusivity that is linearly dependent on time. Such a prediction differs from that of homogeneous turbulence and seems to have some support from experimental data in the earth's atmosphere.