The Reynolds shear stress phase distribution and its relationship to spectral energy density in wall-bounded flows

Distance-from-the-wall scaling is widely understood to play a substantial role in shaping both the kinematics and mean dynamics of wall-bounded flows. Building models around such observations, however, requires a precise understanding of which quantities are affected, where in physical/scale space they are affected, and how the influence of wall-distance is manifested. In this study, we examine the scale-by-scale distribution of Reynolds normal and shear stresses and their dependence on wall-distance in order to better understand the emergence of distance-from-the-wall scaling. Coherence and phase distributions are considered in addition to auto- and co-spectral energy densities, as these reveal additional details regarding wall-distance scaling. It is found that the streamwise and wall-normal velocities are most coherent at zero phase lag, and that the scale at which this balance occurs is proportional to distance from the wall. Finally, results from a wavelet decomposition are shown to evaluate the degree to which self-similarity observed in a mean sense is also observed instantaneously.