In the present study, we investigate the modulation effects of particles on compressible turbulent boundary layers at a Mach number of 6, employing high-fidelity direct numerical simulations based on the Eulerian–Lagrangian point-particle approach. Our findings reveal that the mean and fluctuating velocities in particle-laden flows exhibit similarities to incompressible flows under compressibility transformations and semi-local viscous scaling. With increasing particle mass loading, the reduction in Reynolds shear stress and the increase in particle feedback force constitute competing effects, leading to a non-monotonic variation in skin friction, particularly in turbulence over cold walls. Furthermore, dilatational motions near the wall, manifested as travelling-wave structures, persist under the influence of particles. However, these structures are significantly weakened due to the suppression of solenoidal bursting events and the negative work exerted by the particle feedback force. These findings align with the insight of Yu et al. (J. Fluid. Mech., vol. 984, 2024, A44), who demonstrated that dilatational motions are generated by the vortices associated with intense bursting events, rather than acting as evolving perturbations beneath velocity streaks. The attenuation of travelling-wave structures at higher particle mass loadings also contributes to the reduction in the intensities of wall shear stress and heat flux fluctuations, as well as the probability of extreme events. These results highlight the potential of particle-laden flows to mitigate aerodynamic forces and thermal loads in high-speed vehicles.

We report an experimental study of Rayleigh–Bénard convection of liquid metal GaInSn in a cuboid cell with an aspect ratio of 0.5 under the effect of a horizontal magnetic field. The Rayleigh number spans a range of $3.8\times 10^5 \leqslant Ra \leqslant 1.1\times 10^7$, while the magnetic field strength reaches up to 0.5 T, corresponding to a maximum Hartmann number to 2041. By combining temperature and velocity measurements, we identify several flow morphologies, including a novel cellular pattern characterized by four stacked vortices that periodically squeeze and induce velocity reversals. Based on the identified flow morphologies, we partition the entire ($Ra, Ha$) parameter space into five distinct flow regimes and systematically investigate the flow characteristics within each regime. The temperature gradient and oscillation frequency exhibit scaling relationships with the combined parameters $Ra$ and $Ha$. Notably, we observe a coupling between flow regime and global transport efficiencies, particularly in a regime dominated by the double-roll structure, which experiences a maximum 36 % decrease in heat transfer efficiency compared with the single-roll structure. The dependencies of heat and momentum transport on $Ra$ and $Ha$ follow scaling laws as $Nu \sim (Ha^{-2/3}RaPr^{-1})^{3/5}$ and $Re \sim (Ha^{-1}RaPr^{-1})^{4/3}$, respectively.

The seminal Bolgiano–Obukhov (BO) theory established the fundamental framework for turbulent mixing and energy transfer in stably stratified fluids. However, the presence of BO scalings remains debatable despite their being observed in stably stratified atmospheric layers and convective turbulence. In this study, we performed precise temperature measurements with 51 high-resolution loggers above the seafloor for 46 h on the continental shelf of the northern South China Sea. The temperature observation exhibits three layers with increasing distance from the seafloor: the bottom mixed layer (BML), the mixing zone and the internal wave zone. A BO-like scaling $\alpha =-1.34\pm 0.10$ is observed in the temperature spectrum when the BML is in a weakly stable stratified ($N\sim 0.0018$ rad s$^{-1}$) and strongly sheared ($Ri\sim 0.0027$) condition, whereas in the unstably stratified convective turbulence of the BML, the scaling $\alpha =-1.76\pm 0.10$ clearly deviated from the BO theory but approached the classical $-$5/3 scaling in isotropic turbulence. This suggests that the convective turbulence is not the promise of BO scaling. In the mixing zone, where internal waves alternately interact with the BML, the scaling follows the Kolmogorov scaling. In the internal wave zone, the scaling $\alpha =-2.12 \pm 0.15$ is observed in the turbulence range and possible mechanisms are provided.

Developing a model to describe the shock-accelerated cylindrical fluid layer with arbitrary Atwood numbers is essential for uncovering the effect of Atwood numbers on the perturbation growth. The recent model (J. Fluid Mech., vol. 969, 2023, p. A6) reveals several contributions to the instability evolution of a shock-accelerated cylindrical fluid layer but its applicability is limited to cases with an absolute value of Atwood numbers close to $1$, due to the employment of the thin-shell correction and interface coupling effect of the fluid layer in vacuum. By employing the linear stability analysis on a cylindrical fluid layer in which two interfaces separate three arbitrary-density fluids, the present work generalizes the thin-shell correction and interface coupling effect, and thus, extends the recent model to cases with arbitrary Atwood numbers. The accuracy of this extended model in describing the instability evolution of the shock-accelerated fluid layer before reshock is confirmed via direct numerical simulations. In the verification simulations, three fluid-layer configurations are considered, where the outer and intermediate fluids remain fixed and the density of the inner fluid is reduced. Moreover, the mechanisms underlying the effect of the Atwood number at the inner interface on the perturbation growth are mainly elucidated by employing the model to analyse each contribution. As the Atwood number decreases, the dominant contribution of the Richtmyer–Meshkov instability is enhanced due to the stronger waves reverberated inside the layer, leading to weakened perturbation growth at initial in-phase interfaces and enhanced perturbation growth at initial anti-phase interfaces.

In the present study, we perform direct numerical simulations of compressible turbulent boundary layers at free stream Mach numbers $2\unicode{x2013}6$ laden with dilute phase of spherical particles to investigate the Mach number effects on particle transport and dynamics. Most of the phenomena observed and well-recognized for inertia particles in incompressible wall-bounded turbulent flows – such as near-wall preferential accumulation and clustering beneath low-speed streaks, flatter mean velocity profiles, and trend variation of the particle velocity fluctuations – are identified in the compressible turbulent boundary layer as well. However, we find that the compressibility effects are significant for large inertia particles. As the Mach number increases, the near-wall accumulation and the small-scale clustering are alleviated, which is probably caused by the variations of the fluid density and viscosity that are crucial to particle dynamics. This can be affected by the fact that the forces acting on the particles with viscous Stokes number greater than 500 are modulated by the comparatively high particle Mach numbers in the near-wall region. This is also the reason for the abatement of the streamwise particle velocity fluctuation intensities with the Mach numbers.

In the present study, we performed direct numerical simulations for a hypersonic turbulent boundary layer over the windward side of a lifting body, the HyTRV model, at Mach number $6$ and attack angle 2$^{\circ }$ to investigate the global and local turbulent features, and evaluate its difference from canonical turbulent boundary layers. By scrutinizing the instantaneous and averaged flow fields, we found that the transverse curvature on the windward side of the HyTRV model induces the transverse opposing pressure gradients that push the flow on both sides towards the windward symmetry plane, yielding significant effects of the azimuthal inhomogeneity and large-scale cross-stream circulations, moderate and azimuthal independent influences of adverse pressure gradient, and negligible impact of the mean flow three-dimensionality. Further inspecting the local turbulent statistics, we identified that the mean and fluctuating velocity become increasingly similar to the highly decelerated turbulent boundary layers over flat plates in that the mean velocity deficit is enhanced, and the outer layer Reynolds stresses are amplified as it approaches the windward symmetry plane, and prove to be self-similar under the scaling of Wei & Knopp (J. Fluid Mech., vol. 958, 2023, A9) for adverse-pressure-gradient turbulent boundary layers. Conditionally averaged Reynolds stresses based on strong sweeping and ejection events demonstrated that the Kelvin–Helmholtz instability of the strong embedded shear layer induced by the large-scale cross-stream circulations is responsible for the turbulence amplification in the outer layer. The strong Reynolds analogy that relates the mean velocity and temperature was refined to incorporate the non-canonical effects, showing considerable improvements in the accuracy of such a formula. On the other hand, the temperature fluctuations are still transported passively, as indicated by their resemblance to the velocity. The conclusions obtained in the present study provide potentially profitable information for turbulent modelling modification for the accurate predictions of skin friction and wall heat transfer.

Dilatational motions in the shape of travelling wave packets have been identified recently to be dynamically significant in hypersonic turbulent boundary layers. The present study investigates the mechanisms of their generation and their association with the solenoidal motions, especially the well-recognized near-wall self-sustaining process of the regeneration cycle between the velocity streaks and quasi-streamwise vortices. By exploiting the direct numerical simulation databases and orchestrating numerical experiments, we explore systematically the near-wall flow dynamics in the processes of the formation and transient growth of low-speed streaks. We conclude via theoretical ansatz that the nonlinearity related to the parallel density and pressure gradients close to the wall due to the restriction of the isothermal boundary condition is the primary cause of the generation of the dilatational structures at small scales. In fully developed turbulence, the formation and the existence of healthy dilatational travelling wave packets require the participation of the turbulence at scales larger than those of the near-wall regeneration cycles, especially the occurrence of the bursting events that generate vortex clusters. This is proven by the less intensified dilatational motions in the numerical experiments in which the Orr mechanism is alleviated and the vortical structures and turbulent bursts are weakened.

The classification of internet gaming disorder (IGD) as a mental condition for further study in 2013 marked the emerging recognition of potential mental health issues associated with internet and gaming addiction. The COVID-19 pandemic and the rapid growth of gaming technology have combined to increase internet gaming, resulting in unhealthy lifestyle behaviors, poor sleep quality and psychological distress. Identifying the complex interplay between internet problem use, sleep disorders and psychological distress is crucial. However, it remains unclear how physical activity and self-compassion could improve sleep quality when individuals experience IGD symptoms. The current study, therefore, examined the relationships between IGD, sleep quality, self-compassion, physical activity and psychological distress using a path analysis approach. The study, targeting young adults (N = 283), found that physical activity played a significant role in connecting the variables and supporting the overall fit of the model. The results suggest that interventions targeting individuals with IGD should focus on promoting physical activity participation and developing self-compassion. Future research should continue to investigate the effectiveness of clinical interventions that incorporate self-compassion and physical activity counseling for individuals with IGD.

Nacrite and dickite are found in two localities in northern Taiwan. One, containing nacrite and dickite, is associated with a gold-enargite deposit as a vug-filling clay in the Chinkushih (CKS) mine district near the northern coast. The other is the occurrence of dickite in the interstices of a Miocene coarse-grained quartzose sandstone in the Nanshihchiao (NSC) area, near Taipei city. X-ray diffraction (XRD), differential thermal analysis (DTA), scanning electron microscope (SEM), and petrographic examinations were used to characterize the mineralogical features. Nacrite most often takes the unusual form of rhombic platelets, and dickite is commonly elongated in habit with the shapes possibly related to their origin. Based on geological evidence, we believe that both nacrite and dickite are of hydrothermal origin. In the CKS area, the formation of nacrite and dickite is related to the hypogene gold-enargite mineralization. In contrast, the transformation of dickite in the NSC area is due to the influence of the raised temperatures of sandstone formation, resulting from volcanic activity during the Kungkuan stage after the deposition of the sandstone.

Clay mineral compositions from 2 paleosol profiles (Chu-Wan, CW, and Shiao-Men Yu, SMY, profiles) on the late-Miocene sediments in Penghu Islands (Pescadores), Taiwan, are characterized by random X-ray powder diffraction (XRD) and transmission electron microscopy (TEM). By the clay assemblage of the paleosol profile, we want to explore the probable formation mode of the Penghu paleosols.

The paleosol profiles in study are overlain by a layer of basalt flow. However, the clay mineralogy of the 2 paleosols was not altered metasomatically after burial. Results show that 3 distinctive zones of different dominating kaolin-group minerals are apparent in the profiles. In descending order, they are: 1) spheroidal, hollow 7Å-halloysite, 2) platy, irregular-shaped and disordered kaolinite, and 3) platy, irregular-shaped, disordered kaolinite. The relative crystallinity of kaolin minerals of the 3 layers is: layer 2 > layer 3 > layer 1. On the basis of the XRD, TEM analyses and the crystallinity calculations, the distribution of kaolin in Penghu paleosol profiles appears to be unique. Penghu paleosol profiles show systematic change in kaolin crystallinity and polymorphs with depth. Because the clay type is heterogeneous within the profile, this represents that Penghu paleosol profiles were polypedogenic.

The contact between the upper basalt and the paleosol is the erosion surface, so we do not know exactly what the thickness of the original paleosol was. The first layer (about 20 cm) of the profiles appears to be constituents of the original paleosol. It contains high contents of pedogenic (in situ weathering) hematites and 7Å-halloysites, which implies that the local climate of the Penghu Islands at late Miocene was warm and humid. Intense leaching and dry/wet cycle should be the reason for high contents of halloysite (>60%) in the Penghu paleosols. Laterization was the probable pedogenic process for the formation of the paleosols.

Considering straw resource utilization and air pollution prevention, straw return has been commonly practiced in China. However, the practicability of plenty straw return in an emerging maize–rice rotation and their effects on soil C and N pools have not been extensively investigated. This study has been conducted to examine the effects of straw return on soil nutrients, soil functional C and N fractions, and then to figure out their relationships with yield and N use efficiency. Two treatments of straw return (S2Nck) and without straw return (S0Nck) were compared in 3-year field experiment, and subplots without N application were added in their respective plots in the third year. The results showed that, relative to the control (S0Nck), straw return significantly increased soil mineralized nitrogen (Nmin), available P, and exchange K content by 11.7%, 41.1%, and 17.4% averaged across 3-year experiments, respectively. Straw return substantially increased soil dissolved organic C, microbial biomass C, and microbial biomass N content by 73.0%, 25.2%, and 36.8%, respectively. Furthermore, straw return markedly increased C and N retention in particulate organic matter in microaggregates (iPOM) and mineral associated organic matter within microaggregates (intra-SC), but significantly reduced in free mineral associated organic matter (free-SC) fraction. The structural equation modeling analysis showed that yield and the partial factor productivity of N were positively correlated with labile and slow soil C and N fractions. Consequently, straw incorporation significantly increased grain yields of maize by 14.7% and rice by 15.1%. The annual potential reduction proportion in fertilizer-N induced by straw return was estimated to be 25.7% in the third year. This study suggests that the incorporation of straws is an effective way to enhance soil nutrients and regulate soil C and N pools to improve crop production and has the potential to reduce N fertilizer application under maize–rice rotation in subtropical regions.

Very-large-scale motions are commonly observed in moderate- and high-Reynolds-number wall turbulence, constituting a considerable portion of the Reynolds stress and skin friction. This study aims to investigate the behaviour of these motions in high-speed and high-Reynolds-number turbulent boundary layers at varying Mach numbers. With the aid of high-precision numerical simulations, numerical experiments and theoretical analysis, it is demonstrated that the very-large-scale motions are weakened in high-Mach-number turbulence at the same friction Reynolds numbers, leading to the reduction in turbulent kinetic energy in the outer region. Conversely, the lower wall temperature enhances the very-large-scale motions but shortens the scale separation between the structures in the near-wall and outer regions.

Chinmen Island is located in the west of the Taiwan Strait, 15 km from the coast of mainland China. Mesozoic granitic gneiss forms the basement rocks of the island. High-defect kaolin deposits, both major sedimentary and minor residual types of clays, have been mined for ceramic uses for many years. The objectives of this study were to characterize the kaolin deposits and to discuss the genesis of kaolin minerals on the island. The kaolin samples were characterized by X-ray diffraction and transmission and scanning electron microscopy. In general, the particle-size distribution of the sedimentary kaolin was 0.5–5.0% sand, 15–55% silt and 30–85% clay. In the clay fraction, the ratio of kaolinite to illite ranged from 9:1 to 3:1. The sedimentary kaolin materials were originally transported by river from mainland China. Kaolinite occurred generally as pseudo-hexagonal platelets of ∼1 µm in diameter. The residual kaolin minerals resulted from the argillization of granitoid rocks by in situ weathering which possibly occurred during the Pleistocene. The residual kaolin contained more tubular halloysite.

A typical feature of thermal convection is the formation of large-scale flow (LSF) structures of the order of system size. How this structure affects global heat transport is an important issue in the study of thermal convection. We present an experimental study of the coupling between the flow structure and heat transport in liquid metal convection with different degrees of spatial confinement, characterized by the aspect ratio $\varGamma$ of the convection cell. Combining measurements in two convection cells with $\varGamma =1.0$ and 0.5, the study shows that a large-scale circulation (LSC) transports ${\sim }35\,\%$ more heat than a twisted LSC. It is further found that when the LSF is in the form of the LSC state, the system is in a fully developed turbulence state with a $Nu\sim Ra^{0.29}$ scaling for the heat transport. However, the twisted LSC state with a heat transport scaling of $Nu\sim Ra^{0.37}$ appears when the system is not in the fully developed turbulence state. Bistability is observed when the system evolves from the twisted-LSC-dominated to the LSC-dominated state.

We show theoretically that the usual estimated investment strategies will not achieve the optimal Sharpe ratio when the dimensionality is high relative to sample size, and the $ 1/N $ rule is optimal in a 1-factor model with diversifiable risks as dimensionality increases, which explains why it is difficult to beat the $ 1/N $ rule in practice. We also explore conditions under which it can be beaten, and find that we can outperform it by combining it with the estimated rules when $ N $ is small, and by combining it with anomalies or machine learning portfolios, conditional on the profitability of the latter, when $ N $ is large.

In the present study, we investigate the compressibility effects in supersonic and hypersonic turbulent boundary layers under the influence of wall disturbances by exploiting direct numerical simulation databases at Mach numbers up to 6. Such wall disturbances enforce extra Reynolds shear stress on the wall and induce mean streamline curvature in rough wall turbulence that leads to the intensification of turbulent motions in the outer region. The turbulent and fluctuating Mach numbers, the density and the velocity divergence fluctuation intensities suggest that the compressibility effects are enhanced by the increment of the free-stream Mach number and the implementation of the wall disturbances. The differences between the Reynolds and Favre average due to the density fluctuations constitute approximately $9\,\%$ of the mean velocity close to the wall and $30\,\%$ of the Reynolds stress near the edge of the boundary layer, indicating their non-negligibility in turbulent modelling strategies. The comparatively strong compressive events behaving as eddy shocklets are observed at the free-stream Mach number of $6$ only in the cases with wall disturbances. By further splitting the velocity into the solenoidal and dilatational components with the Helmholtz decomposition, we found that the dilatational motions are organized as travelling wave packets in the wall-parallel planes close to the wall and as forward inclined structures in the form of radiated waves in the vertical planes. Despite their increased magnitudes and higher portion in the Reynolds normal and shear stresses, the dilatational motions show no tendency of contributing significantly to the skin friction and the production of turbulent kinetic energy due to their mitigation by the cross-correlation between the solenoidal and dilatational velocity components.

Instability evolutions of shock-accelerated thin cylindrical SF$_6$ layers surrounded by air with initial perturbations imposed only at the outer interface (i.e. the ‘Outer’ case) or at the inner interface (i.e. the ‘Inner’ case) are numerically and theoretically investigated. It is found that the instability evolution of a thin cylindrical heavy fluid layer not only involves the effects of Richtmyer–Meshkov instability, Rayleigh–Taylor stability/instability and compressibility coupled with the Bell–Plesset effect, which determine the instability evolution of the single cylindrical interface, but also strongly depends on the waves reverberated inside the layer, thin-shell correction and interface coupling effect. Specifically, the rarefaction wave inside the thin fluid layer accelerates the outer interface inward and induces the decompression effect for both the Outer and Inner cases, and the compression wave inside the fluid layer accelerates the inner interface inward and causes the decompression effect for the Outer case and compression effect for the Inner case. It is noted that the compressible Bell model excluding the compression/decompression effect of waves, thin-shell correction and interface coupling effect deviates significantly from the perturbation growth. To this end, an improved compressible Bell model is proposed, including three new terms to quantify the compression/decompression effect of waves, thin-shell correction and interface coupling effect, respectively. This improved model is verified by numerical results and successfully characterizes various effects that contribute to the perturbation growth of a shock-accelerated thin heavy fluid layer.

The oblique shock impinging on the supersonic turbulent boundary layer leads to a mixing layer and the emergence of large-scale coherent structures within the interaction zone which leave significant velocity defect and turbulence amplification downstream. In the present study, we investigate the turbulence recovery in the post-shock region by exploiting direct numerical simulation data of the oblique-shock/turbulent boundary layer interaction flow at the incoming Mach number of $2.28$ and the shock angle of $33.2^\circ$, with special attention paid to the contribution of the mixing layer and large-scale structures to flow dynamics. For that purpose, we propose to split the mean velocity, Reynolds stresses and spanwise spectra into a canonical portion that is constructed according to the statistics of canonical turbulent boundary layers, and a mixing-layer-induced portion. We found that the hidden mixing layer grows with the boundary layer thickness and that the induced mean shear and Reynolds stresses decay at different rates. The mean velocity recovers to the canonical profiles at a distance of 13 boundary layer thicknesses downstream where the mixing-layer-induced mean shear ceases to have strong impacts. The recovery of Reynolds stresses requires 10 boundary layer thicknesses in the near-wall region but a much longer streamwise extent in the outer region due to the slow decay of large-scale motions. These large-scale motions superpose on the near-wall turbulence, intensifying the turbulent fluctuations, yet having a trivial impact on the skin friction, for the contribution of the mixing-layer-induced mean shear and Reynolds shear stress are balanced by the advection term. We further establish a simple physical model capable of approximately predicting the streamwise evolution of mixing-layer-induced mean shear and turbulent kinetic energy. This model suggests that the complete recovery of turbulence in the outer region requires a streamwise extent of approximately 50 boundary layer thicknesses.

This paper presents systematic molecular dynamics modelling of Na-montmorillonite subjected to uniaxial compression and unidirectional shearing. An initial 3D model of a single-cell Na-montmorillonite structure is established using the Build Crystal module. The space group is C2/m, and COMPASS force fields are applied. Hydration analysis of Na-montmorillonite has been performed to validate the simulation procedures, where the number of absorbed water molecules varied with respect to the various lattice parameters. A series of uniaxial compression stress σzz and unidirectional shear stress τxy values are applied to the Na-montmorillonite structure. It is shown that the lattice parameter and hydration degree exhibit significant influence on the stress–strain relationship of Na-montmorillonite. The ultimate strain increases with increases in the lattice parameter but decreases in the number of water molecules. For saturated Na-montmorillonite, more water molecules result in a stiffer clay mineral under uniaxial compression and unidirectional shearing.