A NEW MEAN VELOCITY SCALING FOR TURBULENT BOUNDARY LAYERS

Abstract

A new scaling, originally developed for the mean velocity profile of turbulent pipe flow, was extended to the case of zero pressure gradient turbulent boundary layers. At low Reynolds numbers, the new scaling leads to a power law for the overlap region of the mean velocity profile. At high Reynolds numbers, the conventional overlap region given by a log law is also obtained. Comparisons were made between the power law and 17 velocity profiles covering a large range of Reynolds numbers. This comparison showed that a power law with empirical constants determined from pipe flow data was in good agreement with boundary layer data. A new outer velocity scale was also proposed. The new outer velocity scale was used to normalize the 17 velocity profiles and the collapse of these profiles was significantly better than for profiles normalized by the friction velocity or the freestream velocity.