  We investigate through numerical simulations of the Navier-Stokes equations
the influence of the surface roughness on the fluid flow through fracture
joints. Using the Hurst exponent $H$ to characterize the roughness of the
self-affine surfaces that constitute the fracture, our analysis reveal the
important interplay between geometry and inertia on the flow. Precisely, for
low values of Reynolds numbers Re, we use Darcy's law to quantify the hydraulic
resistance $G$ of the fracture and show that its dependence on $H$ can be
explained in terms of a simple geometrical model for the tortuosity $\tau$ of
the channel. At sufficiently high values of Re, when inertial effects become
relevant, our results reveal that nonlinear corrections up to third-order to
Darcy's law are aproximately proportional to $H$. These results imply that the
resistance $G$ to the flow follows a universal behavior by simply rescaling it
in terms of the fracture resistivity and using an effective Reynolds number,
namely, Re/$H$. Our results also reveal the presence of quasi-one-dimensional
channeling, even considering the absence of shear displacement between upper
and lower surfaces of the self-affine fracture.
