Nonlocal description of turbulent dispersion

Abstract

Although it is common engineering practice to model turbulent mass transport by assuming the turbulent mass flux as proportional to the local mean concentration gradient, it is well known that the applicability of this assumption is very limited, especially when the length scales and time scales of the transport process are not much smaller than the scales of variations in either the velocity or the concentration fields. In the present work the formalism of stochastic Green's functions is used to derive general, nonlocal, integrodifferential equations for turbulent transport that incorporate the multiscale aspects of the phenomena of absolute and relative dispersion. It is shown that the turbulent mass fluxes are in general equal to convolutions over space and time of the mean concentration gradients with space- and time-dependent kernel functions. By introducing different closure approximations for the kernel functions one can obtain in a systematic, deductive, manner a variety of common models for turbulent transport, corresponding to either local or nonlocal descriptions of dispersion.