In dispersed two-phase flows, particle electrification is a prevalent phenomenon that plays a crucial role in particle transport. However, the influences of electrostatic forces on particle behaviour in wall-bounded turbulent flows, especially in bidisperse cases, is not well understood. In this study, using direct numerical simulations based on a coupled Eulerian–Lagrangian point-particle approach at friction Reynolds number $Re_\tau =550$, we demonstrate that when the electrostatic Stokes number is of the order of $O(10^{-1})$, electrostatic forces could considerably alter particle behaviour in both monodisperse and bidisperse particle-laden turbulent channel flows. Specifically, the wall-normal profiles of the particle concentration are determined by the competition of turbophoresis, biased sampling and electrostatic effects. The electrostatic forces are found to reduce the concentrations of lighter particles by electrostatic drift directly, whereas they alter those of heavier particles by strengthening turbophoresis indirectly. With increasing electrical charge, the dynamics of the lighter particles remains approximately unchanged, but that of the heavier particles is modulated significantly due to their relatively strong particle–electrostatic interaction. In the near-wall region, electrostatic forces tend to homogenize the distribution of lighter particles in the spanwise direction by inhibiting the formation and destruction of particle clusterings and voids, thereby maintaining the anisotropic streaky clusterings. Furthermore, even though the clustering dynamics remains unchanged, the spatial extents of the clusterings at the channel centreline are suppressed (enhanced) by a factor of two, probably due to the remarkable reduction (increase) of particle concentration in this layer.

Drag force acting on a particle is vital for the accurate simulation of turbulent multiphase flows, but the robust drag model is still an open issue. Fully resolved direct numerical simulation (DNS) with an immersed boundary method is performed to investigate the drag force on saltating particles in wall turbulence over a sediment bed. Results show that, for saltating particles, the drag force along the particle trajectories cannot be estimated accurately by traditional drag models originally developed for an isolated particle that depends on the particle-wall separation distance or local volume fraction in addition to the particle Reynolds number. The errors between the models and DNS are especially clear during the descending phase of the particles. Through simple theoretical analysis and DNS data fitting, we present a corrected factor using the classical, particle Reynolds number dependent drag force model as the benchmark model. The new drag model, which takes the particle vertical velocity into account, can reasonably predict the mean drag force obtained by DNS along a particle trajectory.

Dust storms are typical dispersed two-phase atmospheric turbulence involving electrified charged dust particles. Previous observations have demonstrated that clean-air atmospheric turbulence is strongly intermittent. However, the intermittency of the wind velocity, concentration of dust particles with a diameter smaller than $10\ \mathrm {\mu }{\rm m}$ (PM10) and electric fields, known as multifield intermittency, has not been reported or characterized yet. Here, we quantify the small-scale multifield intermittency of dust storms using datasets obtained from the Qingtu Lake Observation Array and a wavelet-based data analysis technique. The results indicate that the probability density functions of the multifield increments are scale dependent, and the scaling exponents of the multifield structure functions exhibit anomalous scaling, suggesting that the multiple fields in dust storms are also highly intermittent. Specifically, the wind velocity during dust storms appears to be more intermittent as compared with clean-air conditions. Among the multiple fields, the small-scale intermittency is strongest for PM10 dust concentration, moderate for electric fields and weakest for wind velocity. Furthermore, the anomalous scaling of multiple fields is well described by the hierarchical structure theory of turbulence. It is theoretically predicted that the wind velocity displays a one-dimensional filamentary structure, while the PM10 dust concentration and electric fields display two-dimensional sheet-like structures. Finally, after removing the coherent components of the observed time series by the proposed wavelet conditioning statistics, Kolmogorov linear scaling is recovered for the multiple fields, suggesting that small-scale multifield intermittency is caused by the presence of small-scale coherent structures.

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.

A large-scale spanwise and wall-normal array of sonic anemometers in the atmospheric surface layer is used to acquire all three components of instantaneous fluctuating velocity as well as temperature in a range of stability conditions. These data permit investigation of the three-dimensional statistical structure of turbulence structures. Based on a similar dataset, Krug et al. (Boundary-Layer Meteorol., vol. 172, 2019, pp. 199–214) reported a self-similar range of wall-attached turbulence structures under both unstable and near-neutral stability conditions. They considered only a wall-normal array and thus assessed statistical structure in the wall-normal direction, in relation to the streamwise wavelength. The present work extends the view of a self-similar range of turbulence structures, by including the statistical structure in the spanwise direction. Moreover, by analysing the phase shift between synchronized measurements in the spectral domain, it is inferred how a scale-dependent inclination angle in the streamwise/wall-normal plane varies with stability. Results suggest that the self-similar wall-attached structures have similar aspect ratios between streamwise/wall-normal scales and streamwise/spanwise scales such that $\lambda _x/\Delta z : \lambda _x/\Delta y \approx 1$ for both near-neutral and unstable conditions. Under the most unstable conditions, coherent structures with $\lambda _x/\delta = 1$ are inclined at angles as high as $65^{\circ }$ relative to the solid boundary, while larger scales $\lambda _x/\delta = 6$ exhibit inclination angles of approximately $35^{\circ }$. For near-neutral stability conditions, the angle tends towards $12^{\circ }$ for all scales. It is noted that in the near-neutral condition, the structure inclination angle and the aspect ratio – and thus the statistical modelling of coherent structures in the atmospheric surface layer – are highly sensitive to the value of the stability parameter.

In recent years, observations of the atmospheric surface layer have greatly promoted research on high-Reynolds-number wall-bounded turbulence, especially observations of wind-blown sand flows/sandstorms, which are typical sand-laden two-phase flows; these successes have advanced the science of gas–solid two-phase wall-bounded turbulence to very-high-Reynolds-number conditions. Based on a review of existing atmospheric surface layer observations and the development process, this paper summarizes the important promoting effect played by these observations in understanding the very-large-scale structure characteristics, turbulent kinetic energy fraction and amplitude modulation effect, and in reconstructing the spatial electric field under high-Reynolds-number wall turbulence. This review focuses on the main successes achieved by the observation of sand-laden two-phase flows and the three-dimensional turbulent flow field, especially in the streamwise direction. Finally, some suggestions and outlooks for further research on particle-laden two-phase wall-bounded turbulence under high-Reynolds-number conditions are presented.

Large-eddy simulation of a particle-laden flow over an erodible bed is performed to investigate the effect of heavy, saltating particles on turbulence modulation, using the Eulerian–Lagrangian point-particle approach with two-way coupling. The flow into which the solid particles are introduced is a turbulent open channel flow with particle-free friction Reynolds numbers of 3730 and 4200. The inter-particle collisions are not considered, whereas the particle-bed collisions are described by splashing models. Simulation results show that the addition of particles reduces the mean streamwise fluid velocity. The streamwise fluctuating velocity and Reynolds stress are damped while the vertical and spanwise turbulence intensities are enhanced in the near-bed region. The turbulence intensities and Reynolds stress in the outer layer are apparently increased. These effects become more pronounced as the Reynolds number increases. Correlation scales of the turbulence structures increase in the near-bed region and decrease in the outer region. The modulation mechanism of turbulence is revealed. That is, the range and degree of turbulence enhancement by ascending particles in the near-bed region are much larger than those of turbulence attenuation by descending particles, which results in the redistribution of turbulent kinetic energy from the streamwise to the spanwise and vertical directions. This effect extends to the outer region via saltating particles by forming ‘active’ roughness elements. The premultiplied energy spectra of the streamwise velocity show that the enhancement of outer turbulent kinetic energy by saltating particles occurs in a wide range of wavelengths from the intermediate to very large scale.

The interaction between heavy particles with high Stokes number ($St$) and the wall, known as the particle–wall (P–W) process, widely exists in natural and engineering two-phase flows, whereas its effects on particle-laden flows and the large-scale/very large-scale turbulent motions (VLSM) remain unclear. In this paper, two types of wind-blown sand-laden flows were experimentally designed and investigated by keeping the same free stream velocity, flow Reynolds number and particle $St$ number. In the first type, sand particles were directly blown from a sand bed at the bottom wall of the wind tunnel, and the P–W process occurred in the whole wall-normal region of the sand-laden flow. In the second type, sand particles were released from a feeder at the top wall of wind tunnel, and the P–W process was only present in a lower wall-normal region. Simultaneous two-phase particle image/tracking velocimetry measurements were conducted for uncovering the characteristics of turbulent structures in the particle-laden turbulent boundary layers. The results confirmed that the VLSM with streamwise scales exceeding $3\delta$ ($\delta$ is boundary layer thickness) above a certain height exist in both types of the sand-laden flows and could be significantly affected by the P–W process. That is, in the region without the P–W process, the presence of sand particles can enlarge the VLSM, while in the region with the P–W process, the VLSM are substantially reduced in size or even destroyed. The reduction degree is found to be closely related to the strength of the P–W process.

According to Townsend’s attached eddy hypothesis (AEH), a boundary layer flow is comprised of wall-attached eddies, but to extract the part of the flow whose statistical behaviours are well described by the AEH is not at all straightforward. The objective of this work is to extract the part of the flow that can be described by the AEH, and study the statistical behaviours of the other part, which cannot be described by the AEH. In this process, two types of eddies are identified in addition to the Kolmogorov-scale eddies, i.e. wall-attached eddies and wall-detached eddies. The statistical behaviours of the wall-attached eddies are shown to be very well described by the AEH, i.e. the eddies are wall-attached, self-similar and, importantly, Gaussian, whereas the wall-detached eddies cannot be modelled by the AEH. Specifically, a decomposition scheme is proposed following Townsend (The Structure of Turbulent Shear Flow, Cambridge University Press, 1976). We apply our decomposition scheme to three different flows, i.e. channel, boundary layer and atmospheric surface layer flows. The results are similar with only quantitative differences, suggesting possible universality in both the wall-attached eddies and the wall-detached eddies.

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.

A field observation array for the atmospheric surface layer (ASL) was built on a dry flat bed of Qingtu Lake in Minqin (China) as the Qingtu Lake Observation Array (QLOA) site, which is similar to the Surface Layer Turbulence and Environmental Science Test (SLTEST) site in the Utah (USA) Western desert. The present observation array can synchronously perform multi-point measurements of wind velocity and temperature at different vertical and streamwise positions. In other words, three-dimensional turbulent ASL flows can be measured at the QLOA station and Reynolds numbers as high as $Re_{\unicode[STIX]{x1D70F}}\sim O(10^{6})$ can be achieved with steady wind conditions. By careful selection and pretreatment for measured data of more than 1200 h, the QLOA data have been validated to be reliable for high Reynolds number turbulent boundary layer research. Results from correlation and spectral analysis confirm that very large scale motions (VLSMs) exist in the ASL at a Reynolds number up to $Re_{\unicode[STIX]{x1D70F}}\approx 4\times 10^{6}$. Through premultiplied spectral analysis, it is revealed that the spectral energy in the high-wavenumber region decreases with height, similar to turbulent boundary layers at low or moderate Reynolds numbers, while it increases with height in the low-wavenumber region resulting in a log–linear increase of VLSMs energy with height, which is different from turbulent boundary layers at low or moderate Reynolds numbers. The present analyses support the view that the evolution of the VLSMs cannot be fully attributed to a ‘bottom-up’ mechanism alone, and probably other mechanisms, including a ‘top-down’ mechanism, also play a role.

To investigate whether the effect of maternal dietary protein on offspring lipid metabolism is mediated by microRNA (miRNA), fourteen Meishan sows were fed either low-protein (LP, half of standard protein (SP) level, n 7) or SP (n 7) diets throughout gestation and lactation periods. PPAR-γ and CCAAT/enhancer-binding protein-β (C/EBP-β) protein expression was evaluated. The expression of miRNA predicted to directly target PPAR-γ and C/EBP-β in the subcutaneous fat of offspring at weaning age was determined, and the functions of these potential miRNA were verified. The results showed that piglet body weight and back fat thickness were significantly decreased in the LP group compared with the SP group (P< 0·05). The protein level of PPAR-γ was significantly decreased and C/EBP-β protein expression was also decreased, though not significantly (P= 0·056), in the subcutaneous fat of the LP group. Furthermore, miRNA expression analysis showed that miR-130b, targeting the PPAR-γ 3′-untranslated region (UTR), and miR-374b, targeting the C/EBP-β 3′-UTR, were significantly increased in the LP group compared with the SP group; other candidate regulatory miRNA were expressed similarly in both groups. Dual luciferase activity assay results indicated that miR-130b directly recognised and bound to the 3′-UTR of PPAR-γ and thereby suppressed PPAR-γ gene expression. Similar results were found for miR-374b and the 3′-UTR of C/EBP-β. The present study showed that miR-130b and miR-374b are involved in the effect of maternal dietary protein on offspring lipid metabolism in pigs. These results shed new light on our understanding of the maternal effect on offspring lipid deposition.