A Zonal Similarity Analysis of Velocity Profiles in Wall-Bounded Turbulent Shear Flows

Abstract: It is argued that there are three distinct zones in a wall bounded turbulent flow field dominated by three completely different mechanisms: - An outer region where the velocity profile is determined by the pressure distribution - A highly active wall layer dominated by a sequence of inrush-sweep and ejections, and - An intermediate region well described by the traditional logarithmic law proposed by independently Millikan and Prandtl. The log-law and the wall layer are sometimes referred to as the inner region. Under these conditions, a unique set of normalisation parameters cannot possibly apply to all three zones. The inner region can be more successfully represented by normalising the distance and velocity with the values of these scales at the edge of the wall layer since they are shared by both the wall layer and the log-law region. The application of this similarity analysis has successfully collapsed extensive published data for the inner region covering a range of Reynolds numbers from 3000 to 1,000,000 in a variety of geometries including cylindrical pipes, external boundary layers on flat plates, recirculation regions behind a sudden channel expansion, converging rectangular channels and oscillating pipe flows into a unique curve. The normalisation also collapsed drag reducing flow involving ribblets, power law fluids and viscoelastic fluids onto the standard Newtonian curve.