The Reynolds shear stress phase distribution and its relationship to one-point statistics in wall-bounded flows

Scale-by-scale contributions to the Reynolds shear stress are typically discussed in terms of the co-spectrum of the streamwise and wall-normal fluctuating velocities. This only represents part of the picture, however, since the co-spectrum ignores the (typically non-zero) imaginary component, and thus any mean phase lag between the velocity components. This phase lag is examined in turbulent pipe and boundary layer flows up to friction Reynolds numbers of 10000. It is shown that mean self-similarity and clear distance-from-the-wall scaling extends from the near-wall to at least the middle of the wake region. This relationship is further probed via wavelet decomposition to determine the extent to which it exists in an instantaneous sense. It is shown that the probability densities of several quantities, including the streamwise and wall-normal velocity, depend strongly on this instantaneous phase lag. Similar properties are also examined for velocity-vorticity products related to the mean Reynolds stress gradient.