Large-time behavior of macrodispersion in heterogeneous trending aquifers

Abstract

This paper presents a stochastic analysis of the large-time behavior of macrodispersion in a three-dimensional heterogeneous aquifer with a linear trend in the mean log hydraulic conductivity. To solve the problem analytically, focus is placed on the particular case where the linear trend is aligned in the direction of mean hydraulic head gradient. A spectral approach based on Fourier-Stieltjes representations for the perturbed quantities is used to develop closed-form expressions that describe variability of flow velocity, the second-order mean flow, and asymptotic macrodispersion. The impact of the mean log hydraulic conductivity gradient on these results is examined. It is found that the asymptotic longitudinal and transverse macrodispersion coefficients decrease with the increasing trend gradient of mean log hydraulic conductivity in the case of finite Peclet numbers. This feature is a consequence of the reduction in variability of flow velocity with the trend gradient.