On the transition between distributed and isolated surface roughness and its effect on the stability of channel flow

Abstract

The question of whether a system of roughness elements has to be viewed either as a distributed roughness or a set of individual, hydrodynamically independent roughness elements has been considered. The answer has been given in the context of definition of hydraulic smoothness proposed by Floryan [Eur. J. Mech. B/Fluids 26, 305 (2007)] where a roughness system that cannot destabilize the flow is viewed as hydraulically inactive. Linear stability characteristics have been traced from the distributed to the isolated roughness limits. It has been shown that an increase of distance between roughness elements very quickly stabilizes disturbances in the form of streamwise vortices; however, roughness elements placed quite far apart are able to affect evolution of disturbances in the form of traveling waves. Transition from the distributed to the isolated roughness limit is achieved much faster in the case of roughness elements in the form of “trenches” forming depressions below the reference surface than in the case of roughness elements in the form of “ridges” protruding above the reference surface.