ADVECTION-DIFFUSION IN SPATIALLY RANDOM FLOWS - FORMULATION OF CONCENTRATION COVARIANCE

The concentration c(x,t) of a nonreactive solute undergoing advection and diffusion in a spatially random divergence-free flow field is anal yzed. A leading order formulation for the spatial covariance of the co ncentration,field, <(c'x, t)c'((x) over dot, t)over bar>, is made. Tha t formulation includes the velocity variability induced macrodispersiv e flux of the covariance field, and the smoothing effects of diffusion . Previous formulations of the concentration covariance had dropped at least one of these effects. It is shown that both these effects need to be included to obtain a qualitatively correct description of the co ncentration fluctuations.