Amplitude modulation between multi-scale turbulent motions in high-Reynolds-number atmospheric surface layers

Abstract

Long-term measurements were performed at the Qingtu Lake Observation Array site to obtain high-Reynolds-number atmospheric surface layer flow data ($Re_{\unicode[STIX]{x1D70F}}\sim O(10^{6})$). Based on the selected high-quality data in the near-neutral surface layer, the amplitude modulation between multi-scale turbulent motions is investigated under various Reynolds number conditions. The results show that the amplitude modulation effect may exist in specific motions rather than at all length scales of motion. The most energetic motions with scales larger than the wavelength of the lower wavenumber peak in the energy spectra play a vital role in the amplitude modulation effect; the small scales shorter than the wavelength of the higher wavenumber peak are strongly modulated, whereas the motions with scales ranging between these two peaks neither contribute significantly to the amplitude modulation effect nor are strongly modulated. Based on these results, a method of decomposing the fluctuating velocity is proposed to accurately estimate the degree of amplitude modulation. The corresponding amplitude modulation coefficient is much larger than that estimated by establishing a nominal cutoff wavelength; moreover, it increases log-linearly with the Reynolds number. An empirical model is proposed to parametrize the variation of the amplitude modulation coefficient with the Reynolds number and the wall-normal distance. This study contributes to a better understanding of the interaction between multi-scale turbulent motions and the results may be used to validate and improve existing numerical models of high-Reynolds-number wall turbulence.