TRANSPORT IN MULTISCALE LOG CONDUCTIVITY FIELDS WITH TRUNCATED POWER VARIOGRAMS

Di Federico and Neuman [this issue] investigated mean uniform steady s tate groundwater flow in an unbounded domain with log hydraulic conduc tivity that forms a truncated multiscale hierarchy of statistically ho mogeneous and isotropic Gaussian fields, each associated with an expon ential autocovariance. Here we present loading-Order expressions for t he displacement covariance, and dispersion coefficient, of an ensemble of solute particles advected through such a flow held in two or three dimensions. Both quantities are functions of the mean travel distance s, the Hurst coefficient H, and the low-and high-frequency cutoff int egral scales lambda(l) and lambda(u). The latter two are related to th e length scales of the sampling window (region under investigation) an d sample volume (data support), respectively. If one considers transpo rt to be affected by a finite domain much larger than the mean travel distance, so that s much less than lambda(l) < infinity, then an early preasymptotic regime develops during which longitudinal and transvers e dispersivities grow linearly with a. If one considers transport to b e affected by a domain which increases in proportion to s, then lambda (l) and s are of similar order and a preasymptotic regime never develo ps. Instead, transport occurs under a regime that is perpetually close to asymptotic under the control of an evolving scale lambda(l) simila r to s. We show that if, additionally lambda(u) much less than lambda( l), then the corresponding longitudinal dispersivity grows in proporti on to lambda(l)(1+2H) or, equivalently, s(1+2H). Both these preasympto tic and asymptotic theoretical growth rates are shown to be consistent with the observed variation of apparent longitudinal Fickian dispersi vities with scale. We conclude by investigating the effect of variable separations between cutoff scales on dispersion.