Hydrodynamic dispersion is a key controlling factor of solute transport in heterogeneous
porous media. It critically depends on dimensionality. The asymptotic macrodispersion,
transverse to the mean velocity direction, vanishes only in 2D and not in 3D. Using the
classical Gaussian correlated permeability fields with a lognormal distribution of
variance σY2, the
longitudinal and transverse dispersivities are determined numerically as a function of
heterogeneity and dimensionality. We show that the transverse macrodispersion steeply
increases with σY2 underlying
the essential role of flow lines braiding, a mechanism specific to 3D systems. The
transverse macrodispersion remains however at least two orders of magnitude smaller than
the longitudinal macrodispersion, which increases even more steeply with
σY2. At moderate
to high levels of heterogeneity, the transverse macrodispersion also converges much faster
to its asymptotic regime than do the longitudinal macrodispersion. Braiding cannot be thus
taken as the sole mechanism responsible for the high longitudinal macrodispersions. It
could be either supplemented or superseded by stronger velocity correlations in 3D than in
2D. This assumption is supported by the much larger longitudinal macrodispersions obtained
in 3D than in 2D, up to a factor of 7 for σY2 = 7.56.