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We investigate the transport of a passive tracer in a two-dimensionalstratified random medium with flow parallel and perpendicular to the strata.Assuming a Gaussian random flow with a Gaussian correlation function, it is notonly possible to derive exact expressions for the temporal behaviour of thedispersion coefficients characterising the tracer transport, but also toinvestigate the self-averaging properties of these quantities. We give explicitresults for the dispersion coefficient and its mean square fluctuations as afunction of time. As it turns out, the sample to sample fluctuations which areencoded in the latter quantity remain finite even in the asymptotic limit ofinfinite times, which implies that the given two-dimensional model is notself-averaging.Comment: 14 pages, 4 figure

Stratified disordered media: exact solutions for transport parameters and their self-averaging properties