Solute Dispersion in Multidimensional Periodic Saturated Porous Media

Suppose in a convection‐dispersion equation, governing solute movement in a saturated porous medium of infinite extent, the convection velocity components are periodic functions of spatial coordinates. Then it follows from a general mathematical result that the solute concentration can be asymptotically approximated by a Gaussian density. Two theoretical examples, with and without a constant vertical velocity, are given to illustrate an application of this mathematical result to solute dispersion in a parallel‐bedded, three‐dimensional aquifer of infinite extent. Analytical expressions are obtained for dispersion coefficients in the asymptotic Gaussian approximations in the two examples. The dispersion coefficients functionally depend on a velocity scaling parameter U₀ and a spatial scaling parameter (period) a via their product aU₀, and this functional dependence on aU₀ is different in the two examples. The expressions for dispersion coefficients are formally contrasted and compared with those obtained previously by other authors in a parallel‐bedded infinite aquifer in which the convection velocity is a random field. Some physical implications of dependence of dispersion coefficients on a spatial scaling parameter (i.e., the scale effect) are discussed in the context of modeling in an aquifer with evolving heterogeneities. This interpretation of “scale effect” in dispersion coefficients is contrasted with the preasymptotic interpretation in the current literature.