Two-dimensional simulations incorporating detailed chemistry are conducted for detonation initiation induced by dual hot spots in a hydrogen/oxygen/argon mixture. The objective is to examine the transient behaviour of detonation initiation as facilitated by dual hot spots, and to elucidate the underlying mechanisms. Effects of hot spot pressure and distance on the detonation initiation process are assessed; and five typical initiation modes are identified. It is found that increasing the hot spot pressure promotes detonation initiation, but the impact of the distance between dual hot spots on detonation initiation is non-monotonic. During the initiation process, the initial hot spot autoignites, and forms the cylindrical shock waves. Then, the triple-shock structure, which is caused by wave collisions and consists of the longitudinal detonation wave, transverse detonation wave and cylindrical shock wave, dominates the detonation initiation behaviour. A simplified theoretical model is proposed to predict the triple-point path, whose curvature quantitatively indicates the diffraction intensity of transient detonation waves. The longitudinal detonation wave significantly diffracts when the curvature of the triple-point path is large, resulting in the failed detonation initiation. Conversely, when the curvature is small, slight diffraction effects fail to prevent the transient detonation wave from developing. The propagation of the transverse detonation wave is affected not only by the diffraction effects but also by the mixture reactivity. When the curvature of the triple-point trajectory is large, a strong cylindrical shock wave is required to compress the mixture, enhancing its reactivity to ensure the transverse detonation wave can propagate without decoupling.

The Edgerton crown is an iconic manifestation of drop impact splashing, with its prominent cylindrical edge decorated with detaching droplets. Herein, we identify the formation of an intriguing double-crown, when a high-viscosity drop impacts on a shallow pool of a lower-viscosity immiscible liquid. High-speed imaging shows that after the initial fine horizontal ejecta sheet, the first inner crown emerges vertically from the film liquid. This is followed by the second crown which forms near the outer base of the first crown, as the tip of the horizontally spreading viscous drop approaches the outer free surface. Axisymmetric numerical simulations, using the volume-of-fluid method with adaptive grid refinement, show that the flow squeezed out between the viscous drop and the solid surface, generates two counter-rotating vortex rings, which travel radially outwards together and drive out the second crown through the free surface. The bottom vortex emerges from the separated boundary layer at the solid wall, while the top one detaches from the underside of the viscous drop. We map out the narrow parameter regime, where this ephemeral structure emerges, in terms of viscosity ratio, impact velocity and film thickness.

We investigate the drag reduction effects by two representative blowing/suction-based control methods having different drag reduction mechanisms, i.e. the opposition control and uniform blowing (UB), in a bump-installed turbulent channel flow through direct numerical simulations. We consider two different bulk Reynolds numbers ${\textit {Re}}_b = 5600$ and $12\,600$, and bump heights $h^+ \approx 20$ and $40$. In the opposition-controlled case, the friction drag reduction effect in the case with a bump is similar to that in the case without a bump, while the control effect on the pressure drag is hardly observed. The total drag reduction rate decreases for the higher bump height because the ratio of the pressure drag to the total drag increases as the bump height. In the UB case, UB at $0.1\,\%$ or $0.5\,\%$ of the bulk-mean velocity is imposed on the lower wall with a bump, while the same amount of uniform suction (US) is applied on the upper flat wall to keep the mass flow rate. Although the total friction drag increases due to a detrimental effect of US on the upper wall, the wall-normal motions due to the existence of a bump on the lower wall are suppressed by the UB, so that the pressure drag is decreased, unlike the opposition-controlled case. Due to the difference in the inherent drag reduction mechanisms, the flow separation in the region behind the bump is enhanced by the opposition control, while suppressed by UB.

The critical points of vorticity in a two-dimensional viscous flow are essential for identifying coherent structures in the vorticity field. Their bifurcations as time progresses can be associated with the creation, destruction or merging of vortices, and we analyse these processes using the equation of motion for these points. The equation decomposes the velocity of a critical point into advection with the fluid and a drift proportional to viscosity. Conditions for the drift to be small or vanish are derived, and the analysis is extended to cover bifurcations. We analyse the dynamics of vorticity extrema in numerical simulations of merging of two identical vortices at Reynolds numbers ranging from 5 to 1500 in the light of the theory. We show that different phases of the merging process can be identified on the basis of the balance between advection and drift of the critical points, and identify two types of merging, one for low and one for high values of the Reynolds number. In addition to local maxima of positive vorticity and minima of negative vorticity, which can be considered centres of vortices, minima of positive vorticity and maxima of negative vorticity can also exist. We find that such anti-vortices occur in the merging process at high Reynolds numbers, and discuss their dynamics.

The hydrodynamic interactions between a sedimenting microswimmer and a solid wall have ubiquitous biological and technological applications. A plethora of gravity-induced swimming dynamics near a planar no-slip wall provide a platform for designing artificial microswimmers that can generate directed propulsion through their translation–rotation coupling near a wall. In this work, we provide exact solutions for a squirmer (a model swimmer of spherical shape with a prescribed slip velocity) facing either towards or away from a planar wall perpendicular to gravity. These exact solutions are used to validate a numerical code based on the boundary integral method with an adaptive mesh for distances from the wall down to 0.1 % of the squirmer radius. This boundary integral code is then used to investigate the rich gravity-induced dynamics near a wall, mapping out the detailed bifurcation structures of the swimming dynamics in terms of orientation and distance to the wall. Simulation results show that a squirmer may traverse the wall, move to a fixed point at a given height with a fixed orientation in a monotonic way or in an oscillatory fashion, or oscillate in a limit cycle in the presence of wall repulsion.

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 analyse the small-scale characteristics, such as enstrophy, total strain and normality/non-normality, in the three-dimensional, separated flow around a NACA 0018 wing using direct numerical simulations. The angle of attack is $10^\circ$ and the Reynolds number (based on the chord length) is $Re_c=5000$. The role of non-normality is investigated by performing Schur decomposition of the velocity gradient tensor. We also apply the Schur decomposition to derive new expressions for the production of enstrophy and total strain arising from the mean flow inhomogeneity. We focus on two sections of the flow, across the recirculating zone and along the transitioning shear layer, and compare our results with homogeneous isotropic turbulence (HIT). Within the recirculating region, the non-normality index is approximately 0 (and close to the HIT value), indicating almost equal normal and non-normal contributions. However, in the separating layer non-normal effects strongly dominate, especially in the region of kinetic energy growth. Only in the decay region do the values of the non-normality index gradually approximate HIT values. The production of enstrophy due to vortex stretching is dominated by the mixed (interaction) term, where normal strain stretches non-normal vorticity. The same component also dominates the strain self-amplification term. The contributions of different QR regions to the production terms are also examined. Production due to mean strain rate is triggered upstream compared with production due to fluctuating strain fields.

The settling velocity of frozen hydrometeors in the atmospheric surface layer depends on their inertial and drag properties, and on the intensity of ambient turbulence. Thin, solid and perforated circular disks have been investigated through high-speed imaging, under laboratory conditions, to reproduce the settling of snow plates and dendrites in quiescent and turbulent flows. Different perforations made it possible to test the parameterisation of the fall speed in quiescent air, based on the geometric description of the solidity of the disk cross-sectional area. Interestingly, different falling styles, ranging from stable horizontal to fluttering and tumbling, were observed to depend significantly on the perforation geometry, which resulted in the stabilisation of the particle rotation and in a modulation of the drag coefficient. Ambient turbulence is observed to primarily induce cross-flow drag on the disks settling in the nonlinear regime, causing a reduction of the settling velocity in all cases investigated. Turbulence also manifests a secondary effect on the disk rotational dynamics, in particular when tumbling and stable falling styles co-exist, based on the phase space defined by the Reynolds number $Re$ and the inertia ratio $I^*$. The interaction between ambient turbulence, particle anisotropy and permeability and the likelihood of tumbling is inferred to be the main reason for the observed settling velocity variability of snow dendrites in nature.

Achieving precise control over the dynamic manipulation of a drop using an external magnetic field may face challenges due to the intricate relationship between the induced magnetisation and the inherent magnetic properties of the drop. Here, we put forward a fundamental theory that elucidates the morphology and behaviour of a ferrofluid droplet immersed in a different, viscous fluid when subjected to a uniform external magnetic field. Unlike previous studies, we introduce an asymptotic model that investigates the dynamic evolution of the drop by examining the local magnetisation as a function of the magnetic field itself. This leads to an additional contribution to the interfacial energy, resulting in an excess normal traction at the interface. Our analytical findings highlight the significant impact of saturation magnetisation and initial susceptibility of the ferrofluid on the resulting dynamic characteristics, which are further explored through comprehensive numerical simulations to address deformations beyond the scope of the asymptotic theory. Supported by benchmark numerical and experimental results, our study suggests that higher magnetic fields and/or greater saturation magnetisation can enhance drop elongation and accelerate its settling process. We develop a regime map illustrating various dynamic events based on the magnetic properties, which could have fundamental implications for the design and control of micro-encapsulations across a wide range of applications, including thermal processing, chemical synthesis, analysis and medical diagnostics.