Characteristics of wall-attached motions in open channel flows

Time-resolved particle image velocimetry measurements with sufficient spatial resolutions combined with coherence spectrum analysis were adopted to investigate the geometric and kinematic features of wall-attached motions in open channel flows. Results indicate that the diagnosed streamwise wavelength of wall-attached motions λxWA based on a given near zero coherence spectrum threshold exhibits a constant streamwise wavelength/wall-normal distance ratio accompanied with a roughly constant inclination angle within y+ > ∼100 and y/h ≤ 0.7 [y+ is the inner-scale normalized distance to the wall y with y+ = y/(ν/uτ) (ν is the kinematic viscosity and uτ is the friction velocity) and h is the water depth], meaning that they are geometrically self-similar. However, in the free-surface region, where y/h > 0.7, the diagnosed wall-attached motions are non-self-similar with λxWA increasing more dramatically and reaching up to ∼20h at the free surface, which is comparable to the typical scales of very-large-scale motions therein. The wall-attached motions are demonstrated to be both energetic and stress active. Within y/h < 0.7, the wall-attached motions with the streamwise wavelength greater than λxWA (including both the self-similar and non-self-similar wavelength range portions) carry more than 40% of the streamwise turbulent kinetic energy (TKE) and 30% of Reynolds shear stress. Beyond y/h = 0.7, where the self-similar portions vanish, all the wall-attached motions are non-self-similar wall-attached motions, which themselves still maintain considerable strength even at the free surface and contribute to 25% of the streamwise TKE and 10% of the Reynolds shear stress therein.