Wavelet analysis is employed to examine amplitude-and frequency-modulations in broadband signals. Of particular interest are the streamwise velocity fluctuations encountered in wall-bounded turbulent flows. Recent studies have shown that an important feature of the near-wall dynamics is the modulation of small-scales by large-scale motions. Small-and large-scale components of the velocity time series are constructed by employing a spectral separation scale. Wavelet analysis of the small-scale component decomposes the energy in joint time-frequency space. The concept is to construct a low-dimensional representation of the small-scale time-varying spectrum via two new time series: the instantaneous amplitude of the smallscale energy, and the instantaneous frequency. Having the latter in a time-continuous representation allows a more thorough analysis of frequency modulation. By correlating the large-scale velocity with the concurrent small-scale amplitude and frequency realizations, both amplitude-and frequency-modulations are studied. In addition, conditional averages of the small-scale amplitudeand frequency-realizations depict unique features of the scale-interaction. For both modulation phenomena, the much studied time shifts, associated with peak correlations between the large-scale velocity and small-scale amplitude and frequency traces, are addressed. We confirm that the small-scale amplitude signal leads the large-scale fluctuation close to the wall. It is revealed that the time shift in frequency modulation is smaller

A combination of cross-wire probes with an array of flush-mounted skin-friction sensors are used to study the three-dimensional conditional organisation of large-scale structures in a high-Reynolds-number turbulent boundary layer. Previous studies have documented the amplitude modulation of small-scale motions in response to conditionally averaged large-scale events, but the data are largely restricted to the streamwise component of velocity alone. Here, we report results based on all three components of velocity and find that the small-scale spanwise and wall-normal fluctuations (v and w) and the instantaneous Reynolds shear stress (−uw) are modulated in a very similar manner to that previously noted for the streamwise fluctuations (u). The envelope of the small scale fluctuations for all velocity components is well described by the large-scale component of the u fluctuation. These results also confirm the conditional existence of roll modes associated with the very large-scale or 'superstructure' motions.

Abstract

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