  We investigate the transport of a passive tracer in a two-dimensional
stratified random medium with flow parallel and perpendicular to the strata.
Assuming a Gaussian random flow with a Gaussian correlation function, it is not
only possible to derive exact expressions for the temporal behaviour of the
dispersion coefficients characterising the tracer transport, but also to
investigate the self-averaging properties of these quantities. We give explicit
results for the dispersion coefficient and its mean square fluctuations as a
function of time. As it turns out, the sample to sample fluctuations which are
encoded in the latter quantity remain finite even in the asymptotic limit of
infinite times, which implies that the given two-dimensional model is not
self-averaging.
