NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WASHINGTON DC
The present report deals with the variation of a turbulent velocity profile in flow from rough to smooth wall and vice versa. Expressions obtained for the shear-stress distribution with respect to the distance from the point of junction of the different roughnesses and from the wall distance, are utilized to ascertain the developing velocity distributions. Under simplified assumptions, the use of these formulas renders possible the integration of the motion equations for the shear stress. This calculation is carried out and compared with the experiments. Despite the fact that the assumptions in this particular case do not prove to be wholly correct, comparatively good agreement is achieved in the most important region.
Translated from Umformung eines turbulenten Geschwindigkeitsprofiles, prepared by Zeitschrift fuer angewandte Mathematik und Mechanik (Germany East and West), v19 n2 p87-100, Apr 1939. Text in English.