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.
Particle effects on the amplitude modulation are investigated in this study based on observational data with various mass loading acquired from long-term measurements of aeolian sandstorms in high-Reynolds-number ( $Re_{\tau }\sim O(10^6)$ ) near-neutral atmospheric surface layers. In both particle-laden and unladen flows, in addition to the positive top–down modulation behaviour in the logarithmic region, a significant modulation effect that exists for some specific motions is also found for the single-point amplitude modulation. The most energetic turbulent motions exhibit the strongest modulation effect, and the modulating signals do not change with the small-scale motions being modulated. In particle-laden flows, the length of the most energetic structure is almost constant, thus the scales of the modulating signal and carrier signal are hardly affected by particles. However, the addition of particles changes the distribution of energy between multi-scale turbulent motions. The kinetic energy of the large-scale component is less enhanced than the total kinetic energy by particles. This leads to a reduced energy proportion of the large-scale component and an augmented one of the small-scale component. Moreover, the particles produce a large damping in the degree of the amplitude modulation and move down the positions of the modulating signals and carrier signals corresponding to the strongest inter-layer modulation, but the damping is weakened with the wall-normal distance due to the decreased mass loading. This study may provide a more general insight into the modulation mechanism between multi-scale turbulent motions and the effect of particles on turbulence.
Experiments on particle-free and particle-laden flows with the same incoming velocity were conducted in a horizontal wind tunnel. Three cases of particle-laden flows with different degrees of particle near-wall motions and similar particle volume fractions, including top-release particles, local-laying sand beds and global-laying sand beds, were designed to investigate the effects of collision bounces and impact splashing on turbulence statistics. The top-released particles accelerate the fluid during gravitational settling, but weaken the intensity and reduce the probability of ‘ejection’ and ‘sweep’ events. This leads to a weakened Reynolds stress and a decreased scale of the outer spectral peak at the centre of the logarithmic region, indicating a concentration of energy at small scales. In contrast, the collision bounce and impact splashing slow the fluid but promote the ‘ejection and sweep’ cycle with larger intensity, and thus enhance the Reynolds stress. Meanwhile, the bouncing and splashing generate ascending particles that transport the kinetic energy upwards, resulting in more energetic very-large-scale motions further from the wall. This study reveals the importance of particle motions to turbulence, and contributes to a further insight into the interactions between particles and turbulence in two-phase flows with erodible surfaces.
Based on the high-quality observational data in the Qingtu Lake Observation Array (QLOA), the difference in the energy distribution, the scale of the coherent structures, and the amplitude modulation effect of the wall-normal velocity fluctuations between particle-free and particle-laden flow in the atmospheric surface layer are analyzed. The results show that the presence of particles enhanced the wall-normal turbulence intensity, especially the increase at the top of the logarithmic region is more significant though the particle mass loading decreases with the wall-normal distance. A further insight indicates that the increase in the length scale of the wall-normal fluctuating velocity coherent structure by particles is more significant further from the wall, which is supported by the premultiplied energy spectra and the two-point correlation. This leads to a drastic increase in kinetic energy of the large-scale coherent structures by the particle away from the wall and thus results in increased amplitude modulation effects of large-scale wall-normal velocity fluctuations onto small-scales.
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