Mass dispersion in oscillatory flows is closely tied to various environmental and biological processes, differing markedly from dispersion in steady flows due to the periodic expansion and contraction of particle patches. In this study, we investigate the Taylor–Aris dispersion of active particles in laminar oscillatory flows between parallel plates. Two complementary approaches are employed: a two-time-variable expansion of the Smoluchowski equation is used to facilitate Aris’ method of moments for the pre-asymptotic dispersion, while the generalised Taylor dispersion theory is extended to capture phase-dependent periodic drift and dispersivity in the long-time asymptotic limit. Applying both frameworks, we find that spherical non-gyrotactic swimmers can exhibit greater or lesser diffusivity than passive solutes in purely oscillatory flows, depending on the oscillation frequency. This behaviour arises primarily from the disruption of cross-streamline migration governed by Jeffery orbits. When a steady component is superimposed, oscillation induces a non-monotonic dual effect on diffusivity. We further examine two well-studied shear-related accumulation mechanisms, arising from gyrotaxis and elongation. Although these accumulation effects are less pronounced than in steady flows due to flow unsteadiness, gyrotactic swimmers respond more strongly to the unsteady shear profile, significantly modifying their drift and dispersivity. This work offers new insights into the dispersion of active particles in oscillatory flows, and also provides a foundation for studying periodic active dispersion beyond the oscillatory flow, such as periodic variations in shape and swimming speed.

Particle suspensions at the interface of turbulent liquids are governed by the balance of capillary attraction, strain-induced drag and lubrication. Here, we extend previous findings, obtained for small particles whose capillary interactions are dominated by quadrupolar-mode deformation of the interface, to larger spherical and disc-shaped particles experiencing monopole-dominant capillarity. By combining pair-approach experiments, two-dimensional turbulent flow realizations and particle imaging, we demonstrate that particles experiencing monopole-dominant attraction exhibit enhanced clustering compared with their quadrupole-dominant counterparts. We introduce an interaction scale defined by balancing viscous drag and capillary attraction, which is compared with the particle size and interparticle distance. This allows us to map the clustering behaviour onto a parameter space solely defined by those characteristic length scales. This yields a unified framework able to predict the tendency to cluster (and the concentration threshold for those clusters to percolate) in a vast array of fluid–particle systems.

An experimental investigation is conducted to examine the tonal noise generation and flow structures of under-expanded jets interacting with a flat plate. The study combines surface pressure, far-field noise and time-resolved Schlieren visualisations to analyse jet dynamics across a range of isentropic Mach numbers (1.1–1.44) and jet-to-plate distances ($H/D$ = 1, 1.5 and 2.5). The results reveal a distinctly non-monotonic relationship between plate height and the amplitude of screech and plate-induced tones. This behaviour is governed by the constructive and destructive interference between the direct acoustic feedback waves of the jet and those reflected from the plate surface. This interference dictates whether the inherent screech mechanism is suppressed or a new plate-induced tone is amplified. Dynamic mode decomposition and wavenumber-spectral analysis reveal that the plate interaction disrupts the balance between downstream-propagating Kelvin–Helmholtz instabilities and upstream-travelling acoustic waves, fundamentally altering the jet’s resonant feedback loops. A key contribution of this work is the establishment of a direct link between flow dynamics and acoustics through advanced statistical analysis. It is shown that the plate installation asymmetrically amplifies the energy of coherent structures within the jet’s lower shear layer. Crucially, the energy content of these dominant shear-layer structures is found to be the primary driver of the far-field tonal noise magnitude. These findings provide a deeper understanding of the complex coupling between flow and acoustics in installed supersonic jets and offer refined guidance for the development of noise mitigation strategies.

We investigate the angular dynamics of a single spheroidal particle with large particle-to-fluid density ratio in simple shear flows, focusing on the influence of the fluid-inertial torque induced by slip velocity. A linear stability analysis is performed to examine how the fluid-inertial torque, viscous shear torque and particle inertia affect the various stable rotation modes, including logrolling, tumbling and aligning modes. As particle inertia increases, bistable or tristable rotation modes emerge depending on initial conditions. For prolate spheroids, three distinct stable-mode regimes are identified, i.e. logrolling, tumbling and tumbling–logrolling (TL). The presence of these modes depends on particle shape and inertia. For oblate spheroids, when the Stokes number is small, we observe monostable modes (logrolling, tumbling and aligning) and bistable modes (TL, aligning–logrolling) varying with different factors. As Stokes number increases, the tristable mode (aligning–tumbling–logrolling) of oblate spheroids appears. These results of the stability analysis further highlight the intricate and significant effect of fluid-inertial torque compared with the results in the absence of fluid-inertial torque. When we apply fluid-inertial torque to the point-particle model, we reproduce the stable rotation modes observed in particle-resolved simulations, which validates the present stability analysis.

The present experiments investigated the combustion dynamics of single and coaxial laminar diffusion flames within a closed cylindrical acoustic waveguide, focusing on their response to acoustic forcing at a pressure antinode. Nine alternative fuel injectors were used to examine the effect of injector jet diameter and configuration, tube wall thickness, annular-to-inner area and velocity ratio, and jet Reynolds number (below 100) on flame behaviour under different applied frequencies and pressure perturbation amplitudes. Fundamental flame–acoustic coupling phenomena were identified, all of which involved symmetric flame perturbations. These included sustained oscillatory combustion (SOC), multi-frequency periodic liftoff and reattachment (PLOR), permanent flame lift-off (PFLO) with low-level oscillations, and flame blowoff (BO). The phase lag between acoustic forcing and flame response was quantified, providing valuable insights into the coupling dynamics and transition behaviours. Findings revealed how various geometrical and flow characteristics could affect flame stability and resistance to blowoff, even under similar acoustic forcing conditions. Analysis of high-speed spatiotemporal visible imaging using proper orthogonal decomposition (POD) uncovered additional distinct phase portraits and spectral signatures associated with instability transitions, which, coupled with specific dynamical characteristics, enabled new insights into the relevance of injector geometrical characteristics and flow conditions in addressing acoustically coupled combustion instabilities.

We investigate the energetics of mixing induced by a continuously supplied dense current (density $\rho _0$) propagating beneath a lighter ambient fluid (density $\rho _a$) along a horizontal rigid boundary within a rectangular domain. The flow fields are computed using direct numerical simulations (DNS) performed with the Nek5000 spectral element solver. Mixing is quantified through the temporal evolution of the background potential energy, which exhibits a linear increase over time. This linear trend enables the definition of a dimensionless mixing parameter $\gamma$, representing the rate of background potential energy growth. The value of $\gamma$ depends on the initial density contrast for a fixed volumetric discharge at the source, characterised by the dimensionless source Froude number. The results reveal a non-monotonic dependence of $\gamma$ on the source Froude number, highlighting a complex interaction between flow forcing and mixing efficiency. We find that, under the assumption of uniform mixing along the current’s length, a fraction $\gamma /2$ of the total supplied energy is invested in mixing along a horizontal distance equal to the height of the inlet.

This study compares turbulent channel flows over elastic walls with those over rough walls, to explore the role of the dynamic change of shape of the wall in turbulence. The comparison is made meaningful by generating rough walls from instantaneous configurations of elastic cases. The aim of this comparison is to individually understand the role of fluid–structure interaction effects and the role of wall shape/undulations in determining the overall physics of flow near elastic walls. With an increase in the compliance of the wall, qualitatively similar trends for many of the effects produced by a rough wall are also seen in the elastic wall. However, specific features can be observed for the elastic-wall cases only, arising from the mutual interaction between the solid and fluid, leading to a further increase in drag. To understand them, we look at the turbulent structures, which exhibit clear differences across the various configurations: roughness induces only a slight reduction of streamwise coherency, resulting in a situation qualitatively similar to what is found in classical turbulent channel flows, whereas elasticity causes the emergence of a novel dominant spanwise coherency. Additionally, we explored the effect of vertical disturbances on elastic-wall dynamics by comparing with permeable walls having similar (average) wall-normal velocity fluctuations at the interface. The permeable walls were found to have minimal similarities to elastic walls. Overall, we can state that the wall motion caused by the complex fluid–structure interaction contributes significantly to the flow and must be considered when modelling it. In particular, we highlight the emergence of strong wall-normal fluctuations near the wall, which result in strong ejection events, an attribute not observed for rigid walls.

Gas-phase turbulence in a bubbling gas–solid fluidised bed is modelled using the data from particle-resolved direct numerical simulations. The subgrid particle-induced turbulent kinetic energy (TKE) is modelled as a function of filter width, filtered solid volume fraction, particle Reynolds number and filtered gas-phase strain rate tensor. Within the volume-filtered framework, we demonstrate that the fluid Reynolds stress models originally developed for a homogeneous system remain applicable to the inhomogeneous fluidised bed, provided that the inhomogeneous drag and particle-induced TKE models are used for the dissipation rate interfacial term. An algebraic model for the anisotropy of gas-phase velocity variance is developed by simplifying the proposed Reynolds stress equation model, which incorporates the effects from both filtered slip velocity and filtered fluid strain rate. The new models are shown to agree well with the direct numerical simulation data of clustered particle settling systems, indicating good applicability of our models for various clustered particle-laden flows.

The growth of small perturbations in isotropic turbulence is studied using massive ensembles of direct numerical simulations. These ensembles capture the evolution of the ensemble-averaged flow field and the ensemble variance in the fully nonlinear regime of perturbation growth. Evolution equations for these two fields are constructed by applying the ensemble average operator to the Navier–Stokes equations and used to study uncertainty growth in scale and physical space. It is shown that uncertainty growth is described by a flux of energy from the ensemble-averaged flow to the ensemble variance. This flux is formally equivalent to the subgrid scale (SGS) energy fluxes of the turbulence cascade, and can be interpreted as an inverse uncertainty cascade from small to large scales. In the absence of information sources (measurements), the uncertainty cascade is unsteady and leads to the progressive filtering of the small scales in the ensemble-averaged flow, a process that represents the loss of predictability due to chaos. Similar to the kinetic energy cascade, the uncertainty cascade displays an inertial range with a constant average uncertainty flux, which is bounded from below by the average kinetic energy dissipation. Locally in space, uncertainty fluxes differ from the SGS energy fluxes at the same scale, but both have similar statistics and are significantly correlated with each other in space. This suggests that uncertainty propagation is partly connected to the energy cascade and that they share similar mechanisms. These findings open avenues to model uncertainty propagation in turbulence following an approach similar to the SGS models in large-eddy simulations. This is relevant not only to efficiently assess the reliability and accuracy of turbulence forecasts, but also to design uncertainty-robust reconstruction techniques for data assimilation or SGS modelling.

We numerically investigate the hydrodynamics of an actively heaving flexible foil flapping under a wave surface. The coupled level set and volume-of-fluid method is used to capture the air–water interface, and the immersed-boundary method is used to capture the fluid–structure interaction. A sinusoidal heaving motion is imposed at the foil’s leading edge, and its posterior parts oscillate passively according to its flexible characteristics, allowing dynamic interactions with the wave-induced flow. The propulsive performance of the foil is examined for the influence of three main factors: the ratio of the heaving frequency ($f_{\!f}$) to the wave frequency ($f_w$), the phase difference between the heaving motion and the incident wave ($\mathit \varPhi$) and the submergence depth of the foil ($D$). At $\mathit \varPhi = 0$, the results reveal that the propulsion of the flexible foil benefits from flapping near the wave surface when $f_{\!f}/f_w = 0.5$, and the propulsive efficiency is optimised at $D/L = 1$, where $L$ is the foil’s length. However, when $f_{\!f}/f_w$ = 1.0 and 2.0, the propulsion of the flexible foil is hindered near the wave surface. This hydrodynamic hindrance is closely related to vortex splitting and roll-up phenomena, which induce the formation of a drag wake. By adjusting the phase difference $\mathit \varPhi$, the hindrance in the flexible foil propulsion can be mitigated to enhance propulsive performance. To further understand the relationship between the flapping kinematics and propulsive dynamics, we perform a scaling analysis based on lift force and added mass force, offering good quantification of propulsive performance.

Turbulence accounts for most of the energy losses associated with the pumping of fluids in pipes. Pulsatile drivings can reduce the drag and energy consumption required to supply a desired mass flux, when compared with steady driving. However, not all pulsation waveforms yield reductions. Here, we compute drag- and energy-optimal driving waveforms using direct numerical simulations and a gradient-free black-box optimisation framework. Specifically, we show that Bayesian optimisation is vastly superior to ordinary gradient-based methods in terms of computational efficiency and robustness, due to its ability to deal with noisy objective functions, as they naturally arise from the finite-time averaging of turbulent flows. We identify optimal waveforms for three Reynolds numbers and two Womersley numbers. At a Reynolds number of $8600$ and a Womersley number of 10, optimal waveforms reduce total energy consumption by 22 % and drag by 37 %. These reductions are rooted in the suppression of turbulence prior to the acceleration phase, the resulting delay in turbulence onset, and the radial localisation of turbulent kinetic energy and production towards the pipe centre. Our results pinpoint that the predominant, steady operation mode of pumping fluids through pipes is far from optimal.

We study the mechanics of evaporation and precipitate formation in pure and bacteria-laden sessile whole blood droplets in the context of disease diagnostics. Using experimental and theoretical analysis, we show that the evaporation process has three stages based on evaporation rate. In the first stage, edge evaporation results in a gelated contact line along the periphery through a sol–gel phase transition. The intermediate stage consists of a gelated front propagating radially inwards due to capillary flow and droplet height regression in pinned mode, forming a wet-gel phase. We unearthed that the gelation of the entire droplet occurs in the second stage, and the wet-gel formed contains trace amounts of water. In the final slowest stage, the wet gel transforms into a dry gel, leading to desiccation-induced stress forming diverse crack patterns in the precipitate. Slow evaporation in the final stage is quantitatively measured using evaporation of trace water and associated transient delamination of the precipitate. Using the axisymmetric lubrication approximation, we compute the transient droplet height profile and the erythrocytes concentration for the first two stages of evaporation. We show that the precipitate thickness profile computed from the theoretical analysis conforms to the optical profilometry measurements. We show that the drop evaporation rate and final dried residue pattern do not change appreciably within the parameter variation of the bacterial concentration typically found in bacterial infection of living organisms. However, at exceedingly high bacterial concentrations, the cracks formed in the coronal region deviate from the typical radial cracks found in lower concentrations.

Interfaces subjected to strong time-periodic horizontal accelerations exhibit striking patterns known as frozen waves. In this study, we experimentally and numerically investigate the formation of such structures in immiscible fluids under high-frequency forcing. In the inertial regime – characterised by large Reynolds and Weber numbers, where viscous and surface tension effects become negligible – we demonstrate that the amplitude of frozen waves scales proportionally with the square of the forcing velocity. These results are consistent with vibro-equilibria theory and extend the theoretical framework proposed by Gréa & Briard (2019 Phys. Rev. Fluids 4, 064608) to immiscible fluids with large density contrasts. Furthermore, we examine the influence of both Reynolds and Weber numbers, not only in the onset of secondary Faraday instabilities – which drive the transition of frozen wave patterns toward a homogenised turbulent state – but also in selecting the dominant wavelength in the final saturated regime.

Using high-fidelity numerical simulations based on a lattice Boltzmann framework, the advection-enhanced transport of a passive scalar from a prolate spheroid in simple shear flow has been thoroughly investigated across various parameters, including the spheroid’s aspect ratio, particle-to-fluid density ratio, Reynolds number (defined as ${\textit{Re}}=\textit{GR}^{2}/\nu$, where $G$ is the flow shear rate, $R$ is the radius of a sphere of the same volume as the spheroid and $\nu$ is the kinematic viscosity of the fluid) and Schmidt number (defined as $\textit{Sc}=\nu /D$, where $D$ is the diffusivity of passive scalar transport). The Reynolds number is constrained to the range of 0 ≤ Re ≤ 1, where the prolate spheroid tumbles around its minor axis, aligned with the vorticity axis, in an equilibrium state. Several key findings have emerged: (i) particle inertia significantly influences the uniformity of the spheroid’s tumbling, affecting flow patterns around the spheroid and, consequently, the modes of scalar transport; (ii) both uniform and non-uniform tumbling generate a scalar line in the fluid with elevated scalar concentration, which sweeps through the wake region and merges with clusters of previously formed scalar lines; (iii) fluid passing over the spheroid carries the passive scalar downstream along these scalar lines; (iv) variations in the uniformity of spheroid tumbling result in distinct flow patterns and scalar transport modes, leading to different transport rates; (v) within the studied parameter ranges, increased particle inertia enhances the scalar transport rate; (vi) when particle inertia is minimal, the dimensionless scalar transport rate for different aspect ratios converges to a common dependence on the Péclet number. These phenomena are analysed in detail.

The Weissenberg effect, or rod-climbing phenomenon, occurs in non-Newtonian fluids where the fluid interface ascends along a rotating rod. Despite its prominence, theoretical insights into this phenomenon remain limited. In earlier work, Joseph & Fosdick (1973, Arch. Rat. Mech. Anal. vol. 49, pp. 321–380) employed domain perturbation methods for second-order fluids to determine the equilibrium interface height by expanding solutions based on the rotation speed. In this work, we investigate the time-dependent interface height through asymptotic analysis with dimensionless variables and equations using the Giesekus model. We begin by neglecting inertia to focus on the interaction between gravity, viscoelasticity and surface tension. In the small-deformation scenario, the governing equations indicate the presence of a boundary layer in time, where the interface rises rapidly over a short time scale before gradually approaching a steady state. By employing a stretched time variable, we derive the transient velocity field and corresponding interface shape on this short time scale, and recover the steady-state shape on a longer time scale. In contrast to the work of Joseph and Fosdick, which used the method of successive approximations to determine the steady shape of the interface, we explicitly derive the interface shape for both steady and transient cases. Subsequently, we reintroduce small but finite inertial effects to investigate their interaction with viscoelasticity, and propose a criterion for determining the conditions under which rod climbing occurs. Through numerical computations, we obtain the transient interface shapes, highlighting the interplay between time-dependent viscoelastic and inertial effects.

Flows enabled by phoretic mechanisms are of significant interest in several biological and biomedical processes, such as bacterial motion and targeted drug delivery. Here, we develop a homogenisation-based macroscopic boundary condition that describes the effective flow across a diffusio-phoretic microstructured membrane, where the interaction between the membrane walls and the solute particles is modelled via a potential approach. We consider two cases where potential variations occur (i) at the pore scale and (ii) only in the close vicinity of the boundary, allowing for a simplified version of the macroscopic flow description, in the latter case. Chemical interactions at the microscale are rigorously upscaled to macroscopic phoretic solvent velocity and solute flux contributions, and added to the classical permeability and diffusivity properties of the membrane. These properties stem from the solution of Stokes advection–diffusion problems at the microscale, some of them forced by an interaction potential term. Eventually, we show an application of the macroscopic model to develop minimal phoretic pumps, showcasing its suitability for efficient design and optimisation procedures.

Space–time correlations of velocity and high-Schmidt-number ($Sc \approx 2000$) passive scalar fields are investigated in turbulent pipe flow using particle image velocimetry and planar laser-induced fluorescence, respectively. Both the velocity and scalar fields exhibit characteristic elliptical patterns in their respective space–time correlations. The elliptic approximation model, originally developed for the velocity field, is applied to estimate convection and sweeping velocities for both fields. In both fields, the convection velocity decreases, while the sweeping velocity increases, along the pipe radius. The convection velocity ratio between the scalar and velocity fields shows that high-Schmidt-number scalar fluctuations are advected faster than the velocity fluctuations. Similarly, the sweeping velocity of the scalar fluctuations is found to be larger than that of the velocity fluctuations. Furthermore, the high-Schmidt-number scalar is found to decorrelate more rapidly than the corresponding velocity, with the scalar Taylor microscale distinctly smaller than the velocity Taylor microscale.

Directional freezing of brine is widely found in numerous environmental and industrial settings. Despite extensive studies, the microscopic evolution of ice-brine structures remains unclear. By combining in situ micro-computed tomography visualisation and theoretical analyses, we reveal new details inside the porous ice structure and its evolution towards a cleaner ice layer. We identify three distinct stages characterised by different brine exclusion rates during solidification: a rapid initial stage possibly lasting seconds from nucleation to local equilibrium without long-range heat or mass transfer; a second stage where the system reaches global thermal equilibrium, involving brine expulsion by volume expansion and convection associated with gravity; and a final prolonged stage dominated by diffusion. Comparison between analytical solutions and the migration rates of microstructural features such as brine stripes, columns and pockets extracted from photographic images confirms these understandings. Morphologically, we capture the formation of random striped patterns together with brine columns during downward freezing and brine skirts during upward freezing, all of which gradually transform into vertically aligned polygonal patterns. The volume fraction of brine pockets in porous ice near the cold end reduces to less than 10 % after 22 h in most experiments. The residual brine pockets, however, are not rejected out of the porous ice as fast as predicted by diffusion and remain persistent. Our findings provide new insights into the brine freezing dynamics, with implications ranging from sea ice formation to freeze desalination and general solidification of binary melts.

A new statistical definition for the mean turbulent boundary layer (TBL) thickness is introduced, based on identification of the wall-normal location where the streamwise velocity skewness changes sign, from negative to positive, in the outermost region of the boundary layer. Importantly, this definition is independent of arbitrary thresholds, and broadly applicable, including to past single-point measurements. Furthermore, this definition is motivated by the phenomenology of streamwise velocity fluctuations near the turbulent/non-turbulent interface (TNTI), whose local characteristics are shown to be universal for TBLs under low free-stream turbulence conditions (i.e. with or without pressure gradients, surface roughness, etc.) through large-scale experiments, simulations and coherent structure-based modelling. The new approach yields a TBL thickness that is consistent with previous definitions, such as those based on Reynolds shear stress or ‘composite’ mean velocity profiles, and which can be used practically, e.g. to calculate integral thicknesses. Two methods are proposed for estimating the TBL thickness using this definition: one based on simple linear interpolation and the other on fitting a generalised Fourier model to the outer skewness profile. The robustness and limitations of these methods are demonstrated through analysis of several published experimental and numerical datasets, which cover a range of canonical and non-canonical TBLs. These datasets also vary in key characteristics such as wall-normal resolution and measurement noise, particularly in the critical TNTI region.

Floating particles deform the liquid–gas interface, which may lead to capillary repulsion or attraction and aggregation of nearby particles (e.g. the Cheerios effect). Previous studies employed the superposition of capillary multipoles to model interfacial deformation for circular or ellipsoidal particles. However, the induced interfacial deformation depends on the shape of the particle and becomes more complex as the geometric complexity of the particle increases. This study presents a generalised solution for the liquid–gas interface near complex anisotropic particles using the domain perturbations approach. This method enables a closed-form solution for interfacial deformation near particles with an anisotropic shape, as well as the varying height of the pinned liquid–gas contact line. We verified the model via experiments performed with fixed particles held at the water level with shapes such as a circle, hexagon and square, which have either flat or sinusoidal pinned contact lines. Although in this study we concentrate on the equilibrium configuration of the liquid–gas interface in the vicinity of particles placed at fixed positions, our methodology paves the way to explore the interactions among multiple floating anisotropic particles and, thus, the role of particle geometry in self-assembly processes of floating particles.