Mean flow structure and velocity-bed shear stress maxima phase difference in smooth wall, transitionally turbulent oscillatory boundary layers: Experimental observations

Oscillatory boundary layer (OBL) flows over a smooth surface are studied using laser Doppler velocimetry in a large experimental oscillatory flow tunnel. The experiments cover a range of Reynolds numbers in the transitional regime . Motivated by inconsistencies in the literature, the focus is to shed light regarding the phase shift between the bed shear stress and the free stream velocity maxima. Details of the mean flow structure and turbulence characteristics in transitional OBL flows indicate the emergence of a logarithmic profile, which for appears at the middle of the deceleration and as the increases, it appears for a longer part of the period and for a larger region of the boundary layer. Turbulence statistics profiles approach those of equilibrium, unidirectional boundary layer flows with similar, defined using the local free stream velocity and momentum thickness. Analysis of the ensemble-average bed shear stress variation reveals that for the laminar peak disappears under the effect of the turbulence peak. The presence of the phase lag is discussed using data from this study and the literature, and a revised diagram is introduced for the whole range of flows, from laminar to fully turbulent.