The breaking of internal gravity waves in the abyssal ocean is thought to be responsible for much of the mixing necessary to close oceanic buoyancy budgets. The exact mechanism by which these waves break down into turbulence remains an active area of research and can have significant implications on the mixing efficiency. Recent evidence has suggested that both shear instabilities and convective instabilities play a significant role in the breaking of an internal gravity wave in a high Richardson number mean shear flow. We perform a systematic analysis of the stability of a configuration of an internal gravity wave superimposed on a background shear flow first considered by Howland et al. (J. Fluid Mech., vol. 921, 2021, A24), using direct–adjoint looping to find the perturbation giving maximal energy growth on this evolving flow. We find that three-dimensional, convective mechanisms produce greater energy growth than their two-dimensional counterparts. In particular, we find close agreement with the direct numerical simulations of Howland et al. (J. Fluid Mech., 2021, in press), which demonstrated a clear three-dimensional mechanism causing breakdown to turbulence. The results are shown to hold at realistic Prandtl numbers. At low mean Richardson numbers, two-dimensional, shear-driven mechanisms produce greater energy growth.

Foams and bubbles formed in liquid mixtures have lifetimes longer by several orders of magnitude than in pure liquids of similar viscosities. We have shown recently that this effect results from slight differences in molecular concentrations between bulk and surfaces, which give rise to a thickness-dependent surface tension of liquid films. We present a quantitative description of the enhanced stability of liquid films in binary mixtures, based on experimental data and theoretical analysis. Experiments were performed with mixtures of different natures and compositions: foams of stationary heights were obtained by continuous injection of gas, on one hand, and single bubbles were swollen under the surface of a liquid bath, on the other hand. Remarkably, the lifetimes measured in both experiments exhibit the same variations with mixture composition, and follow a power law with the microscopic length that characterises the amplitude of the thickness-dependent surface tension. In addition, the lifetimes vary with the squared film thicknesses at the onset of bursting. We suggest that two stages occur between the birth of liquid films and their rupture. We show how the thickness-dependent surface tension allows an equilibrium shape to be reached at the end of a first stretching stage. We give an analytical description of this shape, which is fully consistent with experimental findings. We suggest a possible mechanism for final rupture of the film, and discuss it in light of existing theoretical predictions. Finally, we compare the properties of liquid mixtures and surfactant solutions, and in particular their surface rheology.

We consider the downstream development of small amplitude unsteady disturbances on a (Blasius) boundary layer. Two-dimensional disturbances have received much attention in the past, but herein lies an interesting conundrum, namely that two completely disparate families exist. The first, originally found by Lam & Rott and Ackerberg & Phillips, is located deep inside the boundary layer, and decays exponentially downstream with an increasingly short wavelength. The other family, originally found by Brown & Stewartson, is centred at the outer edge of the boundary layer, and exhibits slower decay than the former family. In this paper, we consider three-dimensional disturbances. Initially we mount a downstream ‘marching’ approach based on the ‘boundary-region’ equations, wherein spanwise scales are (notionally) comparable to the boundary-layer thickness. These calculations strongly suggest that disturbance growth is possible downstream, in contrast to two-dimensional disturbances that (on the streamwise length scales considered) all decay. We then mount a (heuristic) numerical investigation, performing a locally parallel eigenmode search at increasing downstream locations. This indicates that, for two-dimensional disturbances, with increasingly downstream locations, progressively more eigenmodes evolve, that are clearly linked to the Lam & Rott and Ackerberg & Phillips family, being spawned from what appears to be the Brown & Stewartson variety. These results also clearly indicate three-dimensionality can have a profound effect on the two-dimensional modes, including the potential for downstream growth. This provides an explanation for the downstream growth witnessed in the downstream-developing calculations, and is then conclusively confirmed by (mathematically rigorous) asymptotic analyses, valid far downstream.

Three-scalar subgrid-scale (SGS) mixing in turbulent coaxial jets is investigated experimentally. The flow consists of a centre jet, an annulus and a co-flow. The SGS mixing process and its dependence on the velocity and length scale ratios of the annulus flow to the centre jet are investigated. For small SGS scalar variance the scalars are well mixed and the initial three-scalar mixing configuration is lost. For large SGS variance, the scalars are highly segregated with a bimodal scalar filtered joint density function (f.j.d.f.) at a range of radial locations. Two competing factors, the SGS variance and the scalar length scale, play an important role for the bimodal f.j.d.f. For the higher velocity ratio cases, the peak value of the SGS variance is higher, thereby resulting in stronger bimodality. For the lower velocity ratio cases, the wider mean SGS variance profiles and the smaller scalar length scale cause bimodal f.j.d.f.s over a wider range of physical locations. The scalar dissipation rate structures have similarities to those of mixture fraction and temperature in turbulent non-premixed/partially premixed flames. The observed SGS mixing characteristics present a challenging test for SGS mixing models as well as provides an understanding of the physics for developing improved models. The results also provide a basis for investigating multiscalar SGS mixing in turbulent reactive flows.

We develop a new model, to our knowledge, for the many-body hydrodynamics of amphiphilic Janus particles suspended in a viscous background flow. The Janus particles interact through a hydrophobic attraction potential that leads to self-assembly into bilayer structures. We adopt an efficient integral equation method for solving the screened Laplace equation for hydrophobic attraction and for solving the mobility problem for hydrodynamic interactions. The integral equation formulation accurately captures both interactions for near touched boundaries. Under a linear shear flow, we observe the tank-treading deformation in a two-dimensional vesicle made of Janus particles. The results yield measurements of intermonolayer friction, membrane permeability and, at large shear rates, membrane rupture. The simulation studies include a Janus particle vesicle in both linear and parabolic shear flows, and interactions between two Janus particle vesicles in shear and extensional flows. The hydrodynamics of the Janus particle vesicle is similar to the behaviour of an inextensible, elastic vesicle membrane with permeability.

The model eukaryotic microalgae Chlamydomonas reinhardtii is well known for its ability to generate bioconvection flows that are associated to intricate concentration patterns. Recently, it was demonstrated that the propensity of these algae to move toward a light source – a phenomenon termed phototaxis – can be exploited to locally concentrate micro-organisms and induce (photo)-bioconvection in algal suspensions by inducing a localised excess of density. In the present study we show experimentally that a cell population in a thin liquid layer self-organises in the presence of a heterogeneous light field and displays remarkable symmetry-breaking instabilities that are ruled by both the width of the light beam and the photo-bioconvection Rayleigh number. Beside circular stable states, fingers, dendrites and wave instabilities are reported, quantified and classified in a general phase diagram. Next, we use lubrication theory to develop an asymptotic model for bioconvection in a thin liquid layer, that includes the influences of both gyrotaxis and phototaxis. We obtain a single nonlinear anisotropic diffusion–drift equation describing the spatiotemporal evolution of the depth-averaged algal population. Analytical and numerical solutions are presented and show a very good agreement with the experimental results. In particular, we show that the dendrite instability arises as a result of a subtle coupling between the nonlinearity of the phototactic response, the gyrotactic effect and the self-induced bioconvective flows. Such complex flow fields might find applications in photo-bioreactors, through the efficient stirring of the harvested biomass.

In a theoretical analysis, we generalise well-known asymptotic results to obtain expressions for the rate of transfer of material from the surface of an arbitrary, rigid particle suspended in an open pathline flow at large Péclet number, ${Pe}$. The flow may be steady or periodic in time. We apply this result to numerically evaluate expressions for the surface flux to a freely suspended, axisymmetric ellipsoid (spheroid) in Stokes flow driven by a steady linear shear. We complement these analytical predictions with numerical simulations conducted over a range of ${Pe} = 10^1\text {--}10^4$ and confirm good agreement at large Péclet number. Our results allow us to examine the influence of particle shape upon the surface flux for a broad class of flows. When the background flow is irrotational, the surface flux is steady and is prescribed by three parameters only: the Péclet number, the particle aspect ratio and the strain topology. We observe that slender prolate spheroids tend to experience a higher surface flux compared to oblate spheroids with equivalent surface area. For rotational flows, particles may begin to spin or tumble, which may suppress or augment the convective transfer due to a realignment of the particle with respect to the strain field.

In an effort to capture the continuous hydraulic jump and flow structure for a jet impinging on a disk, we recently proposed a composite mean-field thin-film approach consisting of subdividing the flow domain into three distinct connected regions of increasing gravity strength (Wang et al., J. Fluid Mech., vol. 966, 2023, A15). In the present study, we further validate our approach, and examine the characteristics and structure of the circular jump and recirculation. The influence of the disk radius is found to be significant, especially in the subcritical region. Below a disk radius, the jump transits from type Ia to type 0 after the recirculation zone has faded. The supercritical flow and jump location are insensitive to the disk size, but the jump length and height as well as the vortex size are strongly affected, all decreasing with decreasing disk radius, exhibiting a maximum with the flow rate for a small disk. The jump is relatively steep with a strong recirculation zone for a high obstacle at the disk edge. Comparison against the Navier–Stokes solution of Askarizadeh et al. (Phys. Rev. Fluids, vol. 4, 2019, 114002; Intl J. Heat Mass Transfer, vol. 146, 2020, 118823) for the weak and intermediate surface tension suggests that the surface tension effect is unimportant for a high obstacle for a jump of type 0 or type Ia. The film thickness at the disk edge for a freely draining film is found to comprise, in addition to a static component (capillary length), a dynamic component: ${h_\infty }\sim {(Fr/{r_\infty })^{2/3}}$ that we establish by minimizing the Gibbs free energy at the disk edge, and, equivalently, is also the consequence of the flow becoming supercritical near the edge. By assuming negligible film slope and curvature at the leading edge of the jump and maximum height at the trailing edge, we show that the jump length is related to the jump radius as ${L_J}\sim Re{(F{r^2}/{r_J}^5)^{1/3}}$. The vortex length follows the same behaviour. The energy loss and conjugate depth ratio exhibit a maximum with the flow rate, which we show to originate from the descending and ascending branches of the supercritical film thickness. The presence of the jump is not necessarily commensurate with that of a recirculation; the existence of the vortex closely depends on the upstream curvature and steepness of the jump. The surface separating the regions of existence/non-existence of the recirculation is given by the universal relation $R{e^{10/3}}F{r^2} = 9r_\infty ^9/50$. The jump can be washed off the edge of the disk, particularly at low viscosity and small disk size. The flow in the supercritical region remains insensitive to the change in gravity level and disk size but is greatly affected by viscosity.

Taylor–Couette (TC) flow, the flow between two independently rotating and co-axial cylinders, is commonly used as a canonical model for shear flows. Unlike plane Couette flow, pinned secondary flows can be found in TC flow. These are known as Taylor rolls and drastically affect the flow behaviour. We study the possibility of modifying these secondary structures using patterns of stress-free and no-slip boundary conditions on the inner cylinder. For this, we perform direct numerical simulations of narrow-gap TC flow with pure inner-cylinder rotation at four different shear Reynolds numbers up to $Re_s=3\times 10^4$. We find that one-dimensional azimuthal patterns do not have a significant effect on the flow topology, and that the resulting torque is a large fraction ($\sim$80 %–90 %) of torque in the fully no-slip case. One-dimensional axial patterns decrease the torque more, and for certain pattern frequency disrupt the rolls by interfering with the existing Reynolds stresses that generate secondary structures. For $Re\geq 10^4$, this disruption leads to a smaller torque than what would be expected from simple boundary layer effects and the resulting effective slip length and slip velocity. We find that two-dimensional checkerboard patterns have similar behaviour to azimuthal patterns and do not affect the flow or the torque substantially, but two-dimensional spiral inhomogeneities can move around the pinned secondary flows as they induce persistent axial velocities. We quantify the roll's movement for various angles and the widths of the spiral pattern, and find a non-monotonic behaviour as a function of pattern angle and pattern frequency.

To elucidate the effect of particle shape on the rheology of a dense, viscous suspension of frictional, non-Brownian particles, experimental measurements are presented for suspensions of polystyrene particles with different shapes in the same solvent. The first suspension is made of spheres whereas the particles which compose the second suspension are globular but with flattened faces. We present results from steady shear and shear-reversal rheological experiments for the two suspensions over a wide range of stresses in the viscous regime. Notably, we show that the rheology of the two suspensions is characterised by a shear-thinning behaviour, which is stronger in the case of the suspension of globular particles. Since the shear-reversal experiments indicate an absence of adhesive particle interactions, we attribute the shear thinning to a sliding friction coefficient which varies with stress as has been observed previously for systems similar to the first suspension. We observe that the viscosity of the two suspensions is similar at high shear stress where small sliding friction facilitates particle relative motion due to sliding. At lower shear stress, however, the sliding friction is expected to increase and the particle relative motion would be associated with rolling. The globular particles attain a higher viscosity at low shear stress than the spherical particles. We attribute this difference to a shape-induced resistance to particle rolling that is enhanced by the flattened faces. Image analysis is employed to identify features of the particle geometry that contribute to the resistance to rolling. It is shown that the apparent rolling friction coefficients inferred from the rheology are intermediate between the apparent dynamic and static rolling friction coefficients predicted on the basis of the image analysis. All three rolling resistance estimates are larger for the globular particles with flat faces than for the spherical particles and we argue that this difference yields the stronger shear thinning of the globular particle suspension.

We present numerical analyses of two-dimensional electrohydrodynamic (EHD) flows of a dielectric liquid between a wire electrode and two plate electrodes with a Poiseuille flow, using direct numerical simulation and global stability analysis. Both conduction and injection mechanisms for charge generation are considered. In this work we focused on the intensity of the cross-flow and studied the EHD flows without a cross-flow, with a weak cross-flow and with a strong cross-flow. (1) In the case without a cross-flow, we investigated its nonlinear flow structures and linear dynamics. We found that the flow in the conduction regime is steady, whereas the flow in the injection regime is oscillatory, which can be explained by a global stability analysis. (2) The EHD flow with a weak cross-flow is closely related to the flow phenomena in an electrostatic precipitator (ESP). Our analyses indicate that increasing the cross-flow intensity or the electric Reynolds number leads to a less stable flow. Based on these results, we infer that one should adopt a relatively low voltage and weak cross-flow in the wire-plate EHD flow to avoid flow instability, which may hold practical implications for ESP. (3) The case of strong cross-flow is examined to study the EHD effect on the wake flow. By comparing the conventional cylindrical wake with the EHD wake in linear and nonlinear regimes, we found that the EHD effect brings forward the vortex shedding in wake flows. Besides, the EHD effect reduces the drag coefficient when the cross-flow is weak, but increases it when it is strong.

Experiments are conducted in water films falling along the bottom wall of a weakly inclined rectangular channel of height $5$ mm in the presence of a laminar counter-current air flow. Boundary conditions have been specifically designed to avoid flooding at the liquid outlet, thus allowing us to focus on the wave dynamics in the core of the channel. Surface waves are excited via coherent inlet forcing before they come into contact with the air flow. The effect of the air flow on the height, shape and speed of two-dimensional travelling nonlinear waves is investigated and contrasted with experiments of Kofman, Mergui & Ruyer-Quil (Intl J. Multiphase Flow, vol. 95, 2017, pp. 22–34), which were performed in a weakly confined channel. We observe a striking difference between these two cases. In our strongly confined configuration, a monotonic stabilizing effect or a non-monotonic trend (i.e. the wave height first increases and then diminishes upon increasing the gas flow rate) is observed, in contrast to the weakly confined configuration where the gas flow is always destabilizing. This stabilizing effect implies the possibility of attenuating waves via the gas flow and it confirms recent numerical results obtained by Lavalle et al. (J. Fluid Mech., vol. 919, 2021, R2) in a superconfined channel.

Understanding the transport of particles immersed in a carrier fluid (bedload transport) is still an exciting challenge. Among the different types of gas–solid flows, when the dynamics of solid particles is essentially dominated by collisions between them, kinetic theory can be considered as a reliable tool to derive continuum approaches from a fundamental point of view. In a recent paper, Chassagne et al. (J. Fluid Mech., vol. 964, 2023, A27) proposed a two-fluid model based on modifications to a classical kinetic theory model (Garzó & Dufty, Phys. Rev. E, vol. 59, 1999, pp. 5895–5911). First, in contrast to the classical model, the model proposed by Chassagne et al. takes into account the interparticle friction not only in the radial distribution function but also through an effective restitution coefficient in the rate of dissipation term of granular temperature. As a second modification, at the top of the bed where the volume fraction is quite small, the model accounts for the saltation regime in the continuum framework. The theoretical results derived from the model agree with discrete simulations for moderate and high densities and they are also consistent with experiments. Thus, the model proposed by Chassagne et al. (J. Fluid Mech., vol. 964, 2023, A27) helps provide a better understanding of the combined impact of friction and inelasticity on the macroscopic properties of granular flows.

A liquid metal flow in the form of a submerged round jet entering a square duct in the presence of a transverse magnetic field is studied experimentally. A range of high Reynolds and Hartmann numbers is considered. Flow velocity is measured using electric potential difference probes. A detailed study of the flow in the duct's cross-section about seven jet's diameters downstream of the inlet reveals the dynamics, which is unsteady and dominated by high-amplitude fluctuations resulting from the instability of the jet. The flow structure and fluctuation properties are largely determined by the value of the Stuart number ${{N}}$. At moderate ${{N}}$, the mean velocity profile retains a central jet with three-dimensional perturbations increasingly suppressed by the magnetic field as ${{N}}$ grows. At higher values of ${{N}}$, the flow becomes quasi-two-dimensional and acquires the form of an asymmetric macrovortex, with high-amplitude velocity fluctuations reemerging.

The post-injection migration of a plume of CO$_{2}$ through an inclined, confined porous layer across which the permeability varies is studied theoretically. We derive a sharp-interface lubrication model which accounts for the capillary trapping of CO$_{2}$ at the receding edge of the plume. Eventually the CO$_{2}$ becomes entirely trapped in the pore throats, and the final run-out distance is a key quantity for determining storage security and efficiency. We deploy asymptotic approximations to show that when the CO$_{2}$ plume migrates a long distance relative to its initial length, the run-out distance is approximately proportional to the permeability at the top of the layer. The permeability structure away from the top boundary is important at early and intermediate times. Dissolution of the CO$_{2}$ and three-dimensional effects are incorporated, which demonstrate that the influence of heterogeneity is quite general. The initial distribution of the CO$_{2}$ at the end of the injection phase also influences the post-injection spreading and trapping. At low injection rates, the CO$_{2}$ remains near the top of the layer so that the end-of-injection plume shape has a small aspect ratio leading to a relatively large run-out length. At very high fluxes, the end-of-injection shape and hence the final run-out distance becomes nearly independent of the injection flux because the role of buoyancy becomes negligible during injection. Our results illustrate the strong control of reservoir heterogeneity on the sweep efficiency of a CO$_{2}$ plume and hence the storage capacity. In many situations, it may be possible to increase the storage volume by injecting at a higher rate.

In turbulence near a free surface, strong vortices attach to the surface, creating surface imprints visible as nearly circular ‘dimples’. By studying these imprints in direct numerical simulation (DNS) data we make two observations. First, the imprints of surface-attached vortices can be very effectively distinguished from other turbulent surface features using two physical features: they are nearly circular in shape, and persist for a long time compared with other pertinent time scales. Secondly, the instantaneous number of surface dimples from surface-attached vortices in an area, $N(t)$, is intimately related to its mean-square surface divergence, $\beta ^2(t)$. We develop a simple and physically transparent computer vision procedure which, using the properties of low eccentricity and longevity, detects and tracks vortices from their surface features only, with sensitivity and accuracy of $90\,\%$ or better. We compare $N(t)$ and $\beta ^2(t)$, finding a normalised cross-correlation of $0.90$, with changes in $N$ lagging around $0.8T_\infty$ behind those in $\beta ^2$ ($T_\infty$ is an integral time scale), confirming the common observation that vortices are spawned by strong upwelling events where $\beta ^2$ is large. These findings suggest that the rate of mass flux across the surface, being closely related to surface divergence, can be estimated remotely in some natural flows using visible free-surface dimples as proxy.