A Theory of Fluid Mixing

Abstract

A recently developed theory of fluid mixing is summarized here. It describes linear advection of a passive scalar by a random velocity field. Asymptotic scaling laws are given, which are consistently derived from leading order results of primitive and renormalized perturbation theory in both the Eulerian and Lagrangian pictures. The theory has been verified by numerical simulation, for moderately large perturbation parameters, and by comparison to an exactly solvable case. The theory is suitable for the description of the passive transport of pollutants in ground water. In this context, the time independent velocity υ is a random field, of nonzero mean υ, with a fluctuation δυ = υ — υ which is used as the perturbation expansion parameter. For the purposes of deriving analytic asymptotics, υ is assumed to be a Gaussian random field. For the simulation studies of this theory, υ is derived from Darcy’s law, with heterogeneous geology specified by a log-normal random permeability field.