Flow in Rough Self-Affine Fractures Joints
  We investigate viscous and non-viscous flow in two-dimensional self-affine fracture joints through direct numerical simulations of the Navier-Stokes equations. As a novel hydrodynamic feature of this flow system, we find that the effective permeability at higher Reynolds number to cubic order, falls into two regimes as a function of the Hurst exponent $h$ characterizing the fracture joints. For $h>1/2$, we find a weak dependency whereas for $h<1/2$, the dependency is strong. A similar behavior is found for the higher order coefficients. We also study the velocity fluctuations in space of a passive scalar. These are strongly correlated on smaller length scales, but decorrelates on larger scales. Moreover, the fluctuations on larger scale are insensitive to the value of the Reynolds number. 
Jos\'e S. Andrade Jr., Asc\^anio D. Ara\'ujo, Fernando A. Oliveira and   Alex Hansen