On the self-averaging of dispersion for transport in quasi-periodic random media

In this study we present a numerical analysis for the self-averaging of the longitudinal dispersion coefficient for transport in heterogeneous media. This is done by investigating the mean-square sample-to-sample fluctuations of the dispersion for finite times and finite numbers of modes for a random field using analytical arguments as well as numerical simulations. We consider transport of point-like injections in a quasi-periodic random field with a Gaussian correlation function. In particular, we focus on the asymptotic and pre-asymptotic behaviour of the fluctuations with the aid of a probability density function for the dispersion, and we verify the logarithmic growth of the sample-to-sample fluctuations as earlier reported in Eberhard (2004 J. Phys. A: Math. Gen. 37 2549–71). We also comment on the choice of the relevant parameters to generate quasi-periodic realizations with respect to the self-averaging of transport in statistically homogeneous Gaussian velocity fields.

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