Reynolds number dependence of the amplitude modulated near-wall cycle

The interaction in turbulent boundary layers between very large scale motions centered nominally in the log region (termed superstructures) and the small scale motions is investigated across the boundary layer. This analysis is performed using tools based on Hilbert transforms. The results, across a large Reynolds number range, show that in addition to the large-scale log region structures superimposing a footprint (or mean shift) on to the near-wall fluctuations, the small-scale structures are also subject to a high degree of amplitude modulation due to the large structures. The amplitude modulation effect is seen to become progressively stronger as the Reynolds number increases.