Amplitude modulation of large-scale structures on small-scale structures in open-channel flows at low-to-moderate Reynolds numbers

The modulation effect of large-scale structures on small-scale structures in the logarithmic region was thoroughly reported by Liu et al. [“Amplitude modulation between multi-scale turbulent motions in high-Reynolds-number atmospheric surface layers,” J. Fluid Mech. 861, 585–607 (2019)], offering a valuable reference for quantifying the interactions between structures of different scales. To investigate the modulation effect of large-scale structures on small-scale motions of open-channel flows across the entire water depth range, high-frequency Tomographic Particle Image Velocimetry measurements were conducted over a range of Reynolds numbers (Reτ = 375–3065). The amplitude modulation effect of the streamwise velocity fluctuations was quantified using single-point amplitude modulation analysis. The results indicate that the amplitude modulation effect is not uniformly present across all turbulent length scales; rather, it predominantly occurs in specific scale interactions. The most energetic motions with scales exceeding the wavelength corresponding to the lower-wavenumber peak in the energy spectrum play a critical role in the amplitude modulation effect; the small-scale motions with scales shorter than the wavelength of the higher wavenumber peak (λx < 6 y) are strongly modulated. Based on these results, a scale decomposition method is proposed to accurately estimate the amplitude modulation intensity. The corresponding amplitude modulation coefficient, defined as the peak RAM, exhibits a continuous decrease with increasing y/H—aside from a slight increase near the free surface—and decreases linearly with increasing friction Reynolds number. An empirical model is proposed to parameterize the variation of the amplitude modulation coefficient as a function of the friction Reynolds number and wall-normal distance, applicable across the entire water depth range in open-channel flows at low-moderate Reynolds numbers. This study provides a significant contribution to the enhanced understanding of the interaction mechanisms between large-scale and small-scale structures in wall-bounded turbulence.