Theoretical analysis of non-Gaussian heterogeneity effects on subsurface flow and transport

Much of the stochastic groundwater literature is devoted to the analysis of flow and transport in Gaussian or multi-Gaussian log hydraulic conductivity fields, Y(x), (x being a position vector). Yet Y, as well as many other variables and their increments Delta Y, are known to be generally non-Gaussian. One common manifestation of non-Gaussianity is that whereas frequency distributions of Y often exhibit mild peaks and light tails, those of increments are generally symmetric with peaks that grow sharper, and tails that become heavier, as separation scale or lag between pairs of Y values decreases. A statistical model that captures these disparate, scale-dependent distributions of Y and Delta Y in a unified and consistent manner has been recently proposed by us. This new generalized sub-Gaussian (GSG) model has the form Y(x) = U(x) G(x) where G(x) is (generally, but not necessarily) a multi-scale Gaussian random field and U(x) is a non-negative subordinator independent of G. The purpose of this paper is to explore analytically lead-order effects that non-Gaussian heterogeneity described by the GSG model have on the stochastic description of flow and transport. Our analysis is rendered mathematically tractable by considering mean uniform steady state flow in an unbounded, two-dimensional domain of mildly heterogeneous Y.