Large-scale streaky structures (LSSs) in a temporally developing compressible turbulent mixing layer are investigated using numerical simulations at convective Mach numbers up to $M_c = 5.0$, corresponding to turbulent Mach numbers approaching 1.0. This significantly extends existing numerical studies of compressible mixing layers, which are typically limited to convective Mach numbers of $M_c \approx 2.0$, far below the flow conditions encountered in practical applications such as rocket engines and hypersonic vehicles. As compressibility increases, the growth rate of the momentum thickness decreases continuously without showing signs of saturation, accompanied by a significant increase in the length of the LSSs. In instantaneous flow field, the length of LSSs can exceed 100 times the vorticity thickness $\delta _\omega$ at $ M_c=4.0$. This behaviour is closely connected to the reduction of the pressure–strain redistribution of turbulent kinetic energy with increasing Mach number. Under strong compressibility, the growth stage is dominated by the streamwise components of production and dissipation, generating long, coherent streaks. As small-scale motions emerge, pressure–strain redistribution intensifies, transferring energy from the streamwise to the vertical and spanwise components and inducing streak meandering and breakdown. In the self-similar regime, production, dissipation and redistribution of kinetic energy reach a dynamic equilibrium. The spanwise scale of the LSSs is weakly affected by compressibility and converges to $0.4\delta _\omega$ with the increase of Mach number. Increasing compressibility enhances flow anisotropy, leading to the progressive reduction of vertical and spanwise turbulent kinetic energy relative to the streamwise component, with the vertical component experiencing a more pronounced reduction.

Wall-bounded turbulent flows consist of multiple zones of relatively uniform streamwise velocity, known as uniform momentum zones (UMZs), separated by thin shear layers across which sharp velocity jumps occur. These zonal-like arrangements form a hierarchy consistent with the self-similar eddies postulated in Townsend’s attached-eddy hypothesis (AEH). However, whether the velocity fields carried by UMZs exhibit the asymptotic behaviours predicted by the AEH remains unclear because UMZs coexist over a wide range of scales. Here, we extract wall-scaled UMZs characterised by the wall-normal distance ($y$) and the friction velocity ($u_\tau$), and examine the velocity fields within them in the context of the AEH. We analyse direct numerical simulation data of turbulent pipe flow at friction Reynolds numbers $\textit{Re}_\tau = 550$–$6000$. The number of UMZs increases logarithmically with $\textit{Re}_\tau$, while their interface velocities span a wide range, reflecting their hierarchical organisation. We identify wall-scaled UMZs exhibiting linear growth of thickness with $y$ and velocity jumps scaled by $u_\tau$. The turbulence statistics associated with these UMZs reveal a common wall-normal range, $5\textit{Re}_\tau ^{-1/2} \lt y/R \lt 0.2$ (where $R$ is the pipe radius), over which the mean velocity follows the logarithmic law and the wall-parallel turbulence intensities exhibit logarithmic variation. Within this range, constant regions emerge in the wall-normal turbulence intensity and the Reynolds shear stress wherever the number of UMZs exceeds its mean. The probability density functions (PDFs) of the velocity fluctuations within the wall-scaled UMZs exhibit $\textit{Re}_\tau$-independent self-similarity, characterised by near-zero skewness across the logarithmic region. Consistently, the Kullback–Leibler divergence remains approximately constant, confirming invariant PDF shapes in $y$. These findings demonstrate that the wall-scaled UMZs are directly related to the logarithmic layer and provide a structural basis for the statistical behaviour of wall-bounded turbulence.

Shear-thinning fluids flowing near rough or wavy walls are common in engineering and biological applications, yet their behaviour remains poorly understood. Direct numerical simulation of highly shear-thinning flows is computationally demanding or even infeasible, so convenient methods for accessing this regime are highly sought after. We partially overcome this challenge for the stability analysis of the laminar base flow in the classical test case of flow in an axisymmetric corrugated pipe by employing a large-Reynolds-number asymptotic analysis. First, we obtain the analytic neutral curve for power-law fluids using only the leading order terms. To improve predictive accuracy and to handle more general Carreau–Yasuda fluids, we then develop an asymptotic preserving reduction (APR) that retains several higher order terms. Both approaches show good agreement with full system results computed using a spectral element solver for moderately shear-thinning fluids, including the streaky characteristics of the perturbation flow fields. Furthermore, we extend the stability predictions to strongly shear-thinning fluids. Using APR with Carreau–Yasuda parameters relevant to the experiments, we find that under certain conditions, the instability can arise even for very small wall undulations.

This study investigates turbulent open-channel flow over spanwise-heterogeneous roughness strips composed of fixed spherical elements, with emphasis on the interaction between roughness-induced secondary currents (SCs) and very-large-scale motions (VLSMs). Direct numerical simulations are performed at friction Reynolds numbers ${\textit{Re}}_{\tau }\approx 492$–$538$, with an additional homogeneous-roughness reference case at ${\textit{Re}}_{\tau }\approx 639$. The roughness strips generate persistent, geometry-locked SCs that organise the mean flow into alternating high- and low-momentum pathways, and substantially enhance form-induced stresses relative to both the smooth-wall and homogeneous-roughness references. Rather than uniformly amplifying large-scale motions, the roughness induces a sign-dependent reorganisation of VLSMs: negative-velocity VLSMs are preferentially concentrated above the roughness strips, whereas positive-velocity VLSMs occur more frequently in the inter-strip regions. Conditional correlations further show that, although VLSMs are preferentially identified in the outer region, their strongest statistical footprint remains closely connected to near-wall regions influenced by SC-driven momentum redistribution. Spectral analyses reveal a dynamically connected two-scale pathway, consisting of an outer-scale organisational footprint at $\lambda _z/h=O(1)$ and a smaller near-wall active scale at $\lambda _z/h\approx 0.3$. These results show that roughness-induced SCs govern both the kinematic organisation and the energy-redistribution pathways of VLSMs in spanwise-heterogeneous open-channel flow.

In this study, the Mach reflection of a detonation wave in 2H$_2$ + O$_2$ + 2Ar over a concave double wedge was experimentally investigated. Three Mach reflection configurations could be observed successively, namely, Mach reflection of a Chapman–Jouguet detonation over the first surface, Mach reflection of an overdriven detonation wave over the second surface, and Mach reflection after the interaction of two triple points. The experimental results indicated that the classical reactive theories based on the straight Mach stem assumption are unable to accurately predict the behaviours of the latter two Mach reflections. The asymptotic triple-point trajectory angle of the secondary Mach reflection, $\chi _2$, is significantly smaller than the theoretical prediction. A curved model for the Mach stem $m_1$ is constructed, introducing a curved Mach stem near the triple point. The Mach stem has a concave curvature, implying a lower overdrive degree and a smaller incident angle, which consequently leads to a reduction in $\chi _2$. Based on the curved Mach stem model, an equivalent wedge angle $\varPhi$ and an equivalent overdrive degree $\overline {\alpha }$ are introduced to predict the value of $\chi _2$. An analytical model for solving the interaction of two triple points was developed. Two different wave structures after the interaction – namely, downward-travelling shock–shock and downward-travelling centred shock–expansion – were determined using gas dynamic and shock dynamic methods. The curved Mach stem $m_1$ can result in the variation of the wave structure.

Microfluidic systems integrated with magnetic manipulation of microparticles, serving as a functional component, have been extensively used in various applications, including biomedical diagnostics and targeted drug delivery. Microparticle dynamics in confined microchannels is governed by hydrodynamic viscous effects, magnetic dipole interactions and enhanced interactions with microchannel boundaries, while an in-depth understanding of the underlying mechanisms is still evolving. This work presents a systematic investigation on the dynamic response of microparticles suspended in a quasi-stationary liquid within a microchannel under an external magnetic field using a three-dimensional lattice Boltzmann model (LBM). The hydrodynamic viscous effects and the two-way fluid–structure interaction are fully resolved in this model. A dimensionless analysis of the microparticle dynamic equation is performed first, leading to the identification of two key characteristic parameters central to this work: the magnetic number $N_{\textit{mag}}$, which characterises the synergy of the hydrodynamic viscous effect and the magnetic dipole interaction, and the particle–wall separation distance $R/l$, which accounts for the microchannel wall interaction. Further, a series of LBM simulations with different $N_{\textit{mag}}$ and $R/l$ are carried out. The results suggest that the spatial trajectories of microparticles remain unaffected in response to variation in $N_{\textit{mag}}$, while their aggregation times demonstrate a linear dependence on the reciprocal of $N_{\textit{mag}}$ when released from the same initial position. Moreover, vortices generated by the motion of microparticles within microchannels tend to migrate toward the microparticles themselves as they approach the microchannel walls. As a result, microparticles experience an enhanced hydrodynamic viscous effect, which prolongs their aggregation time and leads to slight deviations in their spatial trajectories. A predictive model for the aggregation time is established, accounting for the effects of the external magnetic field, the microchannel wall interaction, as well as the initial positions of microparticles. The findings in this work provide significant insights into the optimisation of microparticle-based microfluidic technologies, thereby promoting their development in biomedical and chemical analytical applications.