Onset of turbulence in channel flows with scale-invariant roughness

Abstract

Using 3D direct numerical simulations of the Navier–Stokes equations, we study the effect of a self-affine wall roughness on the onset of turbulence in channel flow. We quantify the dependence of the turbulent intensity (proportional to the mean-squared velocity fluctuations) on the Reynolds number Re for different roughness amplitudes A. We find that for sufficiently high amplitudes, A>Ab, the transition changes its nature from being subcritical (as is known at A=0) to supercritical, i.e., the boundary roughness renders the flow unstable for Re>Rel, where the critical Rel decays nontrivially with increasing A. The dependence of the friction factor on Re is found to follow a generalized Forchheimer law, which interpolates between the laminar and inertial asymptotes. The transition between these two asymptotes occurs at a second critical Rec which is comparable in magnitude to Rel. This implies that transitional flow is an integral part of flow in open fractures when Re is sufficiently high, and should be accounted for in effective modeling approaches.