  The evolution and spatial structure of displacement fronts in fractures with
self-affine rough walls are studied by numerical simulations. The fractures are
open and the two faces are identical but shifted along their mean plane, either
parallel or perpendicular to the flow. An initially flat front advected by the
flow is progressively distorted into a self-affine front with Hurst exponent
equal to that of the fracture walls. The lower cutoff of the self-affine regime
depends on the aperture and lateral shift, while the upper cutoff grows
linearly with the width of the front.
