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.

Wall-attached and wall-detached eddies in wall-bounded turbulent flows

“…The results suggest that, at a given wall-normal location, the main inter-scale interaction is among the detached eddies and the small-scale eddies. A recent study using the QLOA dataset also reported a similar one-point multi-scale amplitude-modulation phenomenon (Liu et al 2019).…”

“…A. Yang and X. Zheng 10 3 10 5 10 7 10 2 10 4 10 6 10 3 10 5 10 7 10 2 10 4 10 6 10 3 10 5 10 7 10 2 10 4 10 6 inter-scale interaction of amplitude modulation, where the (loosely defined) small-scale eddies are modulated by the (loosely defined) large-scale eddies. This form of inter-scale interaction has received considerable attention in the recent literature (Hutchins & Marusic 2007;Mathis et al 2009;Chung & McKeon 2010;Guala, Metzger & McKeon 2011;Ganapathisubramani et al 2012;Agostini & Leschziner 2014;Anderson 2016;Dogan, Hanson & Ganapathisubramani 2016;Pathikonda & Christensen 2017Howland & Yang 2018;Liu, Wang & Zheng 2019). In anticipation of the results, we briefly review one of the previously used quantifications of amplitude modulation in Mathis et al (2009): where u S and u L are the (loosely defined) small-and large-scale components of the streamwise velocity, E(•) is the envelope of the bracketed signal and STD(•) is the standard deviation of the bracketed quantity.…”

Large-scale structures of wall-bounded turbulence in single- and two-phase flows: advancing understanding of the atmospheric surface layer during sandstorms

“…This may be because the addition of sand particles into a two-phase flow does not change the scales of the most energetic motions but does change the distribution of energy between turbulent motions at different scales. In E5-22 H. Liu and X. Zheng addition, Liu, Wang, and Zheng (2019b) proposed that not all of the length scales of turbulent motions have an amplitude modulation effect among them; rather, several specific motions have an effect: the most energetic motions with scales larger than the wavelength of the energy spectral peak in the lowerwavenumber region contribute significantly to the amplitude modulation effect, while the motions with small scales (shorter than the wavelength of the higher-wavenumber peak) are strongly modulated. Marusic, Mathis, et al (2010) proposed the Marusic-Mathis-Hutchins (MMH) near-wall wind velocity prediction model, the basic idea of which is to superpose and modulate a large-scale structure in the outer region onto a small-scale structure near the wall to predict the fluctuating wind velocity signal near the wall, which is typically difficult to measure.…”

Experimental study on the effects of particle–wall interactions on VLSM in sand-laden flows

“…It was suggested that the energy transfer of the VLSM may not only be related to the ‘bottom-up’ mechanism (Kim & Adrian 1999), but also the ‘top-down’ mechanism (Hunt & Morrison 2000). After that, Zheng's group revealed that it is the friction velocity rather than the Reynolds number affecting the inclination of the VLSM (Liu, Bo & Liang 2017 a ), and revealed a multiscale amplitude modulation of the turbulent structures (Liu, Wang & Zheng 2019). In addition to the studies on the VLSM in the context of single-phase flows, for the first time, Zheng et al.…”