This study investigates the transport of particles in turbulent channel flow with friction Reynolds number $Re_\tau = 1000$ by direct numerical simulation. We focus on how large-scale flow structures, namely the $Qs$ structures (Lozano-Durán et al. 2012, J. Fluid Mech., vol. 694, pp. 100–130), affect the wall-normal transport of particles. Despite occupying less than $10\,\%$ of the physical domain, our results highlight the critical role played by $Qs$ structures in the particle transport, namely that the particle number and momentum flux inside the $Qs$ structures are substantially higher than outside. The fraction of particle wall-normal momentum flux inside $Qs$ structures is considerably larger than their volume fraction, suggesting highly efficient transport inside the $Qs$ structures. This prominent role played by $Qs$ structures in the transport of inertial particles is more effective by diminishing the inertia of particles. Notably, the long-distance transport of particles in the wall-normal direction is driven primarily by the continuous effect of $Qs$ structures. In summary, our findings advance the understanding of the effects of $Qs$ structures on particle transport, and demonstrate their significant role in the process.

Volcanic fissure eruptions typically start with the opening of a linear fissure that erupts along its entire length, following which, activity localises to one or more isolated vents within a few hours or days. Localisation is important because it influences the spatiotemporal evolution of the hazard posed by the eruption. Previous work has proposed that localisation can arise through a thermoviscous fingering instability driven by the strongly temperature dependent viscosity of the rising magma. Here, we explore how thermoviscous localisation is influenced by the irregular geometry of natural volcanic fissures. We model the pressure-driven flow of a viscous fluid with temperature-dependent viscosity through a narrow fissure with either sinusoidal or randomised deviations from a uniform width. We identify steady states, determine their stability and quantify the degree of flow enhancement associated with localised flow. We find that, even for relatively modest variations of the fissure width (${\lt } 10$ %), the non-planar geometry supports strongly localised steady states, in which the wider parts of the fissure host faster, hotter flow, and the narrower parts of the fissure host slower, cooler flow. This geometrically driven localisation differs from the spontaneous thermoviscous fingering observed in planar geometries and can strongly impact the localisation process. We delineate the regions of parameter space under which geometrically driven localisation is significant, showing that it is a viable mechanism for the observed localisation under conditions typical of basaltic eruptions, and that it has the potential to dominate the effects of spontaneous thermoviscous fingering in these cases.

Ocean submesoscales, flows with characteristic size $10\,\text{m}{-}10\,\text{km}$, are transitional between the larger, rotationally constrained mesoscale and three-dimensional turbulence. In this paper, we present simulations of a submesoscale ocean filament. In our case, the filament is strongly sheared in both vertical and cross-filament directions, and is unstable. Instability indeed dominates the early behaviour with a fast extraction of kinetic energy from the vertically sheared thermal wind. However, the instability that emerges does not exhibit characteristics that match the perhaps expected symmetric or Kelvin–Helmholtz instabilities, and appears to be non-normal in nature. The prominence of the transient response depends on the initial noise, and for large initial noise amplitudes, saturates before symmetric instability normal modes are able to develop. The action of the instability is sufficiently rapid – with energy extraction from the mean flow emerging and peaking within the first inertial period ($\sim\! 18\ \text{h}$) – that the filament does not respond in a geostrophically balanced sense. Instead, at all initial noise levels, it later exhibits vertically sheared near-inertial oscillations with higher amplitude as the initial minimum Richardson number decreases. Horizontal gradients strengthen only briefly as the fronts restratify. These unstable filaments can be generated by strong mixing events at pre-existing stable structures; we also caution against inadvertently triggering this response in idealised studies that start in a very unstable state.

Direct numerical simulations have been conducted to explore the coupling effect of the thermoelectric effect and vertical convection (VC) in a square cavity composed of liquid lithium and stainless steel under different Hartmann numbers at $Ra=10^5$. By leveraging thermoelectric phenomena, an innovative approach is proposed to actively modulate heat transfer efficiency. The core concept lies in modulating the intensity of large-scale circulation (LSC) in VC systems through the torque generated by the interaction between thermoelectric currents and magnetic fields via Lorentz forces. The findings reveal that when the torque aligns with the direction of LSC induced by pure buoyancy, both momentum and heat transfer are enhanced. However, due to the magnetic damping itself, this enhancement is not sustained indefinitely, resulting in a trend of initial increase followed by decline in both momentum and heat transfer efficiency. Conversely, when the magnetic field direction is reversed, causing the Lorentz force torque to oppose the buoyancy-driven circulation, both momentum and heat transfer efficiency diminish until the flow reverses. By varying the magnetic field intensity, three distinct flow regimes are identified: the buoyancy-dominated regime, the thermoelectric-dominated regime and the magnetic-damping-dominated regime. The transition between the buoyancy-dominated regime and thermoelectric-dominated regime – specifically, the onset of flow reversal – is analysed through a boundary-layer–bulk–boundary-layer coupling model. This model enables precise prediction of the critical $Ha$ based on the torque balance between buoyancy forces and thermoelectrically induced Lorentz forces, and demonstrates close agreement with numerical simulations.

We present the results of a theoretical investigation of orbital stability in pilot-wave hydrodynamics, wherein a droplet bounces and self-propels across the surface of a vertically vibrating liquid bath. A critical notion in pilot-wave hydrodynamics is that the bath plays the role of the system memory, recording the history of the droplet in its wave field. Quantised orbital motion may arise when the droplet is confined by either an axisymmetric potential or the Coriolis force induced by system rotation. We here elucidate the dependence of the stability of circular orbits on both the form of the confining force and the system memory. We first provide physical insight by distinguishing between potential- and wave-driven instabilities. We demonstrate that the former are a generic feature of classical orbital dynamics at constant speed, while the latter are peculiar to pilot-wave systems. The wave-driven instabilities are marked by radial perturbations that either grow monotonically or oscillate at an integer multiple of the orbital frequency, in which case they are said to be resonant. Conversely, for potential-driven wobbling, the instability frequency may be resonant or non-resonant according to the form of the applied potential. Asymptotic analysis rationalises the different stability characteristics for linear-spring and Coriolis forces, the two cases that have been explored experimentally. Our results are generalised to consider other potentials of interest in pilot-wave hydrodynamics, and elucidate the distinct roles of wave- and potential-driven instabilities. Our study highlights the limitations of prior heuristic arguments for predicting the onset of orbital instability.

The present work experimentally investigates the interaction of a buoyant (rigid) spherical particle with a single translating (water) vortex ring, focusing on the effects of particle-to-vortex core size ratio ($D_p/D_{c,o}$) on both the particle dynamics and ring dynamics ($D_p$ = particle diameter, $D_{c,o}$ = vortex core diameter). These interactions are studied for $D_p/D_{c,o}$ = 0.6–1.7, over ring Reynolds numbers ($Re={\varGamma }/{\nu }$; $\varGamma$ = ring circulation) of 6000–67 300. As the buoyant particle comes close to the ring, it gets captured into the low-pressure vortex core, and the interaction begins. The particle within the core undergoes radial oscillation, spins and translates along the ring’s azimuthal axis. As $D_p/D_{c,o}$ increases, the particle undergoes higher-amplitude radial oscillation and a relatively shorter azimuthal translation. The differences in the particle size and its motion within the ring lead to large differences in the ring’s dynamics. A larger particle is seen to lead to a higher ring disruption, substantially reducing the ring’s convection speed and azimuthal enstrophy, which are seen to scale as $(D_p/D_{c,o})^{2.3}Re^{-0.37}$ and $(D_p/D_{c,o})^{1.3}Re^{-0.25}$, respectively. The ring disruption is significant above $D_p/D_{c,o}\approx$ 1.0, beyond which the ring fragments, with up to 60 % drop in convection speed and 90 % drop in enstrophy, at low $Re$, as compared with the base ring. These results for the rigid particle size effects on the vortex ring dynamics are more dramatic than for a deforming bubble. Our results could help to better understand and model buoyant particle (and bubble) interactions with coherent structures in turbulence.

This paper presents a theoretical investigation of vortex modes in acoustofluidic cylindrical resonators with rigid boundaries and viscous fluids. By solving the Helmholtz equation for linear pressure, incorporating boundary conditions that account for no-slip surfaces and vortex and non-vortex excitation at the base, we analyse both single- and dual-eigenfunction modes near system resonance. The results demonstrate that single-vortex modes generate spin angular momentum exclusively along the axial direction, while dual modes introduce a transverse spin component due to the nonlinear interaction between axial and transverse ultrasonic waves, even in the absence of vortex excitation. We find that nonlinear acoustic fields, including energy density, radiation force potential and spin, scale with the square of the shear wave number, defined as the ratio of the cavity radius to the thickness of the viscous boundary layer. Theoretical predictions align closely with finite element simulations based on a model for an acoustofluidic cavity with adiabatic and rigid walls. These findings hold particular significance for acoustofluidic systems, offering potential applications in the precise control of cells and microparticles.

The existing studies on vortex rings have concentrated on non-zero circulation. However, the cases of zero circulation may also be significantly noteworthy on both theoretical and practical grounds. As the first attempt on this subject, in this paper a family of viscous laminar vortex rings with zero circulation and a moderate ratio of core radius to ring radius is studied using numerical simulations of the incompressible Navier–Stokes equations. This unusual zero circulation is achieved by assigning a special layered vorticity distribution with alternate signs to the vortex core. At the initial moment, the ring is axisymmetric, swirl-free and of a circular cross-section. It is found that the axial symmetry and the non-swirl nature of the vortex ring are preserved during the evolution, and the vortex ring endures a transition from the initial layered structure to a shell structure, then degenerates to an ordinary vortex ring with non-zero circulation at last. Significant vorticity cancellation is observed due to the interactions among the layered structures. A new Reynolds number, based on the absolute value of vorticity, is applied to the zero-circulation vortex rings in the present work. For such vortex rings, cases of both zero and non-zero vortical impulse can happen, unlike the ordinary ones with only non-zero vortical impulse. Additionally, it is found that the vortical impulse can be irrelevant to the ring diameter. The study may shed light on modelling certain real flows characterised by distinct vortex structures or configurations.

Non-spherical bubble collapses near solid boundaries, generating water hammer pressures and shock waves, were recognized as key mechanisms for cavitation erosion. However, there is no agreement on local erosion patterns, and cavitation erosion damage lacks quantitative analysis. In our experiments, five distinct local erosion patterns were identified on aluminium sample surfaces, resulting from the collapse of laser-induced cavitation bubbles at moderate stand-off distances of $0.4\leqslant \gamma \leqslant 2.2$, namely bipolar, monopolar, annular, solar-halo and central. Among them, the bipolar and monopolar patterns exhibit the most severe cavitation erosion when the toroidal bubbles undergo asymmetrical collapse along the circumferential direction during the second cycle. Shadowgraphy visualization revealed that asymmetrical collapse caused shockwave focusing through head-on collision and oblique superposition of wavefronts. This led to the variations in toroidal bubble radii and the positions of maximum erosion depth not matching at certain stand-off distances. Both initial plasma asymmetry and bubble–wall stand-off distance were critical in determining circumferential asymmetrical collapse behaviours. At large initial aspect ratios, the elliptical jet tips form during the contraction process, resulting in the toroidal bubble collapsing from regions with smaller curvature radii, ultimately converging to the colliding point along the circumferential direction. Our three-dimensional simulations using OpenFOAM successfully reproduce the key features of circumferentially asymmetrical bubble collapse. This study provides new insights into the non-spherical near-wall bubble collapse dynamics and provides a foundation for developing predictive models for cavitation erosion.