Modelling the behaviour of homogeneous scalar turbulence

Abstract

The paper considers the problem of calculating the statistical characteristics of a passive scalar dispersed by a homogeneous turbulence field. In many turbulent shear flows the time-scale for the evolution of the scalar field is intrinsically related to that of the turbulent velocity field. This is by no means always the case, however, and it is at this more general situation that the present work is aimed. An approximate transport equation for the rate of dissipation of scalar variance is proposed which, it is argued, must contain (at least) two sink terms one of which responds to the time scale of the velocity field while the other reflects that of the scalar field itself. The model has been applied to the limited number of homogeneous scalar flows for which data are available and achieves satisfactory agreement as judged by the evolution of the mean-square scalar variance.