Manipulation of small-scale particles across streamlines is the elementary task of microfluidic devices. Many such devices operate at very low Reynolds numbers and deflect particles using arrays of obstacles, but a systematic quantification of relevant hydrodynamic effects has been lacking. Here, we explore an alternative approach, rigorously modelling the displacement of force-free spherical particles in vortical Stokes flows under hydrodynamic particle–wall interaction. Certain Moffatt-like eddy geometries with broken symmetry allow for systematic deflection of particles across streamlines, leading to particle accumulation at either Faxen field fixed points or limit cycles. Moreover, particles can be forced onto trajectories approaching channel walls exponentially closely, making possible quantitative predictions of particle capture (sticking) by short-range forces. This rich, particle-size-dependent behaviour suggests the versatile use of inertia-less flow in devices with a long particle residence time for concentration, sorting or filtering.

Dean’s approximation for curved pipe flow, valid under loose coiling and high Reynolds numbers, is extended to study three-dimensional travelling waves. Two distinct types of solutions bifurcate from the Dean’s classic two-vortex solution. The first type arises through a supercritical bifurcation from inviscid linear instability, and the corresponding self-consistent asymptotic structure aligns with the vortex–wave interaction theory. The second type emerges from a subcritical bifurcation by curvature-induced instabilities and satisfies the boundary region equations. A connection to the zero-curvature limit was not found. However, by continuing from known self-sustained exact coherent structures in the straight pipe flow problem, another family of three-dimensional travelling waves can be shown to exist across all Dean numbers. The self-sustained solutions also possess the two high-Reynolds-number limits. While the vortex–wave interaction type of solutions can be computed at large Dean numbers, their branch remains unconnected to the Dean vortex solution branch.

We report laboratory experiments of long-crested irregular water surface waves propagating over a shoal, with attention to the region over the down-slope behind the shoal. We measure the surface elevation field, the horizontal velocity field in the water, and the resulting forces on a horizontal submerged cylinder placed over the down-slope of the shoal. In addition, we calculate the horizontal acceleration field. From this, we find that the presence of the shoal can modify the wave field such that the resulting forces on the submerged cylinder can be enhanced with thicker extreme tails and increased values of skewness and kurtosis depending on the location of the cylinder. The spatial dependence of the statistics of forces is different from the spatial dependence of the statistics of horizontal velocity, horizontal acceleration and surface elevation.

Highly resolved simulations reveal the fundamental influence of a carrier fluid’s flow dynamics on triboelectric powder charging. We found that particles transported through a square-shaped duct charge faster than in a channel flow caused by secondary flows that led to more severe particle–wall collisions. Specifically, particles with a Stokes number of 4.69 achieve 85 % of their equilibrium charge approximately 1.5 times faster in duct flow than in channel flow. Also, charge distribution is more uniform in a duct cross-section compared with a channel cross-section. In channel flow, particles are trapped near the walls and collide frequently due to limited movement in the wall-normal direction, causing localized charge buildup. In contrast, duct flow promotes better mixing through secondary flows, reducing repeating collisions and providing uniform charge distribution across the cross-section. Upon charging, electrostatic forces significantly reshape particle behaviour and distribution. Once the powder achieves half of its equilibrium charge, particles increasingly accumulate at the wall, leading to a reduced concentration in the central region. These changes in particle distribution have a noticeable impact on the surrounding fluid phase and alter the overall flow dynamics. These findings open the possibility for a new measure to control powder charging by imposing a specific pattern.

The encapsulation of active particles, such as bacteria or active colloids, inside a droplet gives rise to a non-trivial shape dynamics and droplet displacement. To understand this behaviour, we derive an asymptotic solution for the fluid flow about a deformable droplet containing an active particle, modelled as a Stokes-flow singularity, in the case of small shape distortions. We develop a general solution for any Stokes singularity and apply it to compute the flows and resulting droplet velocity due to common singularity representations of active particles, such as Stokeslets, rotlets and stresslets. The results show that offsetting of the active particle from the centre of the drop breaks symmetry and excites a large number of generally non-axisymmetric shape modes as well as particle and droplet motion. In the case of a swimming stresslet singularity, a run-and-tumble locomotion results in superdiffusive droplet displacement. The effect of interfacial properties is also investigated. Surfactants adsorbed at the droplet interface counteract the internal flow and arrest the droplet motion for all Stokes singularities except the Stokeslet. Our results highlight strategies to steer the flows of active particles and create autonomously navigating containers.

We present a linear analysis of a minimal model of moist convection under a variety of atmospheric conditions. The stationary solutions that we analyse include both fully saturated and partially unsaturated atmospheres in both unconditionally and conditionally unstable cases. We find that all of the solutions we consider are linearly unstable via exchange of stability when sufficiently driven. The critical Rayleigh numbers vary by over an order of magnitude between unconditionally unstable and conditionally unstable atmospheres. The unsaturated atmospheres are notable for the presence of linear gravity wave-like oscillations even in unstable conditions. We study their eigenfunction structure and find that the buoyancy and moisture perturbations are anticorrelated in $z$, such that regions of negative buoyancy have positive moisture content. We suggest that these features in unsaturated atmospheres may explain the phenomenon of gravity wave shedding by moist convective plumes.

Liquid metal flows are important for many industrial processes, including liquid metal batteries (LMBs), whose efficiency and lifetime can be affected by fluid mixing. We experimentally investigate flows driven by electrical currents in an LMB model. In our cylindrical apparatus, we observe a poloidal flow that descends near the centreline for strong currents, and a poloidal flow that rises near the centreline for weak currents. The first case is consistent with electrovortex flow, which is an interaction between current and its own magnetic field, whereas the second case is consistent with an interaction between current and the external field, which drives Ekman pumping. Notably, we also observe an intermediate case where the two behaviours appear to compete. Comparing results with Frick et al. (2022 J. Fluid Mech. 949, A20), we test prior estimates of the scaling of flow speed with current to predict the observed reversal. Based on these data, we propose two different ways to apply the Davidson et al. (1999 J. Fluid Mech. 245, 669–699) poloidal suppression theory that explain both experimental results simultaneously: either taking the wire radius into account to scale the Lorentz force, or taking viscous dissipation into account to scale the swirl velocity, following Herreman et al. (2021 J. Fluid Mech. 915, A17).

In this study, we conducted interface-capturing high-resolution simulations of a bubbly upflow in a vertical channel to investigate the bubble distribution and its interaction with surrounding turbulence, focusing on the effects of the density ratio. A bulk Reynolds number $Re_b=2300$ was used for all simulations. The influence of density ratio on vortex structures and turbulence statistics differed between the near-wall and core regions of the channel. Adding 5.43 $\%$ gas caused an increase in wall friction. By applying a generalised FIK identity to analyse wall friction, it was determined that the drag rise in the bubbly channel was mostly due to the near-wall region. Visualisation of the bubble and vortex structures showed that small bubbles near the wall induced larger magnitude of Reynolds shear stress and increased wall friction. Bubble behaviour near the wall region was similar for density ratios above 30, leading to wall friction saturation. In the core region, large deformable bubbles created wake vortices due to slip velocity between liquid and gas phases. Wake vortices help large bubbles absorb smaller bubbles and maintain their sizes. As the density ratio increased, the slip velocity increased owing to greater difference in the gravitational acceleration between liquid and gas phases, resulting in corresponding increase in wake intensity and velocity fluctuations. However, quadrant analysis showed that Q1 and Q3 events increased together with Q2 and Q4 events in the core region, cancelling out any net effect of wake vortices on Reynolds shear stress or wall friction.

Combustion instability analysis in annular systems often relies on reduced-order models that represent the complexity of combustion dynamics in a framework in which the flame is represented by a ‘flame describing function’ (FDF), portraying its heat release rate response to acoustic disturbances. However, in most cases, FDFs are only available for a limited range of disturbance amplitudes, complicating the description of the saturation process at high oscillation levels leading to the establishment of a limit cycle. This article shows that this difficulty may be overcome using a novel experimental scheme, relying on injector staging and in which the oscillation amplitude at limit cycle can be controlled, enabling us to measure FDFs from simultaneous pressure and heat release rate recordings. These data are then exploited to replace the standard modelling, in which the heat release rate is expressed as a third-order polynomial of pressure fluctuations, by a function of the modulation amplitude, allowing an easier adaptation to experimental data. The FDF is then used in a dynamical framework to analyse a set of staging configurations in an annular combustor, where two families of injectors are mixed and form different patterns. The limit-cycle amplitudes and the coupling modes observed experimentally are suitably retrieved. Finally, an expression for the growth rate is derived from the slow-flow variable equations defining the modal amplitudes and phase functions, which is shown to exactly agree with that obtained previously by using acoustic energy principles, providing a theoretical link between growth rates and limit-cycle amplitudes.

The dynamics of a stratified fluid in which the rotation vector is slanted at an angle with respect to the local vertical (determined by gravity) is considered for the case where the aspect ratio of the characteristic vertical scale of the motion D to the horizontal scale L is not small. In cases where the Rossby number of the flow is small the natural coordinate system is non-orthogonal and modifications to the dynamics are significant. Two regimes are examined in this paper. The first is the case in which the horizontal length scale of the motion, L, is sub-planetary where the quasi-geostrophic approximation is valid. The second is the case where the horizontal scale is commensurate with the planetary radius and so the dynamics must be formulated in spherical coordinates with imposing a full variation on the relevant components of rotation. In the quasi-geostrophic case the rotation axis replaces the direction of gravity as the axis along which the geostrophic flow varies in response to horizontal density gradients. The quasi-geostrophic potential vorticity equation is most naturally written in a non-orthogonal coordinate system with fundamental alterations in the dynamics. Examples such as the reformulation of the classical Eady problem are presented to illustrate the changes in the nature of the dynamics. For the second case where the horizontal scale is of the order of R, the planetary radius, more fundamental changes occur leading to more fundamental and difficult changes in the dynamical model.

A new temporal vortex tracking algorithm allows the first long-term temporal observation of the lives of the intense vorticity structures (IVS). The algorithm is applied to direct numerical simulations of statistically stationary isotropic turbulence, with Taylor-based Reynolds numbers in the range $54 \leqslant Re_{\lambda } \leqslant 239$. In the highest Reynolds number case, the continuous time tracking of millions of ‘worms’ is achieved for more than seven integral time scales and close to 200 Kolmogorov time scales. Within an integral scale volume, more than 66 structures exist, and approximately 20 new structures are created per Kolmogorov time. More than $80\, \%$ of the structures live a solitary ‘life’ without any visible interaction with the other structures, while approximately $15\, \%$ break into new structures. Less than $2\, \%$ of the structures merge with others to form new vortices. A ‘population model’ is developed to estimate the numbers of existing vortices for very long simulated times, and it is observed that the birth rate density of these structures slowly increases with the Reynolds number. The survival functions of the IVS lives exhibit an exponential distribution, with some structures living for more than $35$ Kolmogorov time scales (more than four integral time scales). The mean lifetime of the IVS scales with the mean turnover time scale of the worms, defined by their radii and tangential velocity, attaining $\approx 6.5$ turnover time scales at high Reynolds numbers.