Wavelet analysis of broadband signals to extract amplitude and frequency modulation: An application to wall turbulence

Large-scale structures in wall-bounded turbulent flows are known to exhibit a coupling with the small-scale energy in the flow. Besides a superposition of large-scale energy onto the near-wall dynamics, this coupling comprises an amplitude and frequency modulation of the small-scale fluctuations by the large-scale motions. In this work we use wavelet analysis to examine amplitude and frequency modulation. Albeit the wavelet-based approach for amplitude modulation condenses to analyses presented in earlier studies, the strength of the approach becomes evident from a convenient extension of the technique to extract local instantaneous frequency modulation. While discrete techniques were employed previously, an application of a continuous approach results in inherent advantages when phase lags between the large- and small-scale fluctuations in terms of amplitude and frequency modulation are investigated