  The permeability anisotropy that results from a shear displacement 'u'
between the complementary self-affine walls of a rough fracture is
investigated. Experiments in which a dyed fluid displaces a transparent one as
it is radially injected into a transparent fracture exhibit a clear anisotropy
in the presence of shear displacements, and allow us to estimate the ratio of
the permeabilities for flows parallel and perpendicular to 'u'. A simple model
which accounts for the development of channels perpendicular to 'u'
qualitatively explains these results, and predicts a permeability decreasing
(increasing) linearly with the variance of the aperture field for flow parallel
(perpendicular) to the shear displacement. These predictions are then compared
to the results of numerical simulations performed using a lattice-Boltzmann
technique and to the anisotropies measured in displacement experiments.
