Shear stress statistics and wall similarity analysis in turbulent boundary layers using a high-resolution 3-D ADVP

Three-dimensional (3-D) quasi-instantaneous acoustic Doppler velocity profiles at the center of uniform, turbulent open-channel flow over smooth and rough beds have been analyzed for the dynamics of coherent structures. The qualitative aspects of simultaneously measured Eulerian velocity and shear stress signatures identify coherent structures in the water column. A cumulant discard method is applied to describe the statistical properties of the covariance terms u´w´ along the mean flow and v´w´ across the mean flow relative to their time means. Conditional statistics and conditional sampling are used to compare the theoretical and experimental relative covariance contributions from the four quadrants in the longitudinal and transverse planes. The results in the (u´, w´) plane show the dominance of ejections (quadrant 2; u´<0, w´>0) and sweeps (quadrant 4; u´>0, w´<0). In contrast, the distribution of fractional v´w´ events in the transverse plane is quasi-uniform over the four quadrants. Based on these experimentally determined statistical properties of the covariance terms in different flow conditions, a simplified form of the vertical turbulent energy flux in the intermediate flow region is given and the concept of wall similarity in turbulent boundary layers is validated. Since the validity of the wall similarity concept over a wide range of bed roughness has been shown, it is proposed to determine the mean bed friction velocity from the evaluation of the vertical turbulent energy flux.