Effect of roughness on the velocity profile of a laminar boundary layer

Flow past a rough wall is examined. Calculations are made to find the roughness-induced mean velocity which is expressed in an integral form in terms of the spectral density of the roughness and an influence function. Values of the influence function are tabulated using the known values of the modified Hankel functions of order 1/3 and their integrals. The first order change in lower critical Reynolds number due to the roughness-induced change in profile is calculated; the stability of the profile is increased due to the presence of roughness. This work was supported by U.S. Naval Ordnance Systems Command under Contract NOw 65-0123-d through the Garfield Thomas Water Tunnel, Ordnance Research Laboratory.