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.

Research on water wave metamaterials based on local resonance has advanced rapidly. However, their application to floating structures for controlling surface gravity waves remains underexplored. In this work, we introduce the floating metaplate, a periodic array of resonators on a floating plate that leverages locally resonant bandgaps to effectively manipulate surface gravity waves. We employ the eigenfunction matching method combined with Bloch’s theorem to solve the wave–structure interaction problem and obtain the band structure of the floating metaplate. An effective model based on averaging is developed, which agrees well with the results of numerical simulation, elucidating the mechanism of bandgap formation. Both frequency- and time-domain simulations demonstrate the floating metaplate’s strong wave attenuation capabilities. Furthermore, by incorporating a gradient in the resonant frequencies of the resonators, we achieve the rainbow trapping effect, where waves of different frequencies are reflected at distinct locations. This enables the design of a broadband wave reflector with a tuneable operation frequency range. Our findings may lead to promising applications in coastal protection, wave energy harvesting and the design of resilient offshore renewable energy systems.

Flutter in lightweight airfoils under unsteady flows presents a critical challenge in aeroelastic stability and control. This study uncovers phase-dependent effects that drive the onset and suppression of flutter in a freely pitching airfoil at low Reynolds number. By introducing targeted impulsive stiffness perturbations, we identify critical phases that trigger instability. Using phase-sensitivity functions, energy-transfer metrics and dynamic mode decomposition, we show that flutter arises from phase lock-on between structural and fluid modes. Leveraging this insight, we design an energy-optimal, phase-based control strategy that applies transient heaving motions to disrupt synchronisation and arrest unstable growth. This minimal, time-localised control suppresses subharmonic amplification and restores stable periodic motion.

In biology, cells undergo deformations under the action of flow caused by the fluid surrounding them. These flows lead to shape changes and instabilities that have been explored in detail for single component vesicles. However, cell membranes are often multicomponent in nature, made up of multiple phospholipids and cholesterol mixtures that give rise to interesting thermodynamics and fluid mechanics. Our work analyses shear flow around a multicomponent vesicle using a small-deformation theory based on vector and scalar spherical harmonics. We set up the problem by laying out the governing momentum equations and the traction balance arising from the phase separation and bending. These equations are solved along with a Cahn–Hilliard equation that governs the coarsening dynamics of the phospholipid–cholesterol mixture. We provide a detailed analysis of the vesicle dynamics (e.g. tumbling, breathing, tank-treading and swinging/phase-treading) in two regimes – when flow is faster than coarsening dynamics (Péclet number ${\textit{Pe}} \gg 1$) and when the two time scales are comparable ($\textit{Pe} \sim O(1)$) – and provide a discussion on when these behaviours occur. The analysis aims to provide an experimentalist with important insights pertaining to the phase separation dynamics and their effect on the deformation dynamics of a vesicle.

In this investigation, the effect of Ekman pumping on a quasi-geostrophic (QG) system is explored via the vertical buoyancy flux. The vertical buoyancy flux is the quantity in QG flows that is responsible for the adiabatic transfer between kinetic energy (KE) and available potential energy (APE), as well as the slow-time evolution of the mean buoyancy. Ekman pumping (or suction) is a phenomenon that arises through conservation of mass at no-slip boundaries of rotating fluid systems. Three-dimensional QG numerical simulations are run with and without Ekman pumping at the bottom boundary, as well as with and without a realistic stratification profile. Through theory and numerical experiment, it is shown that Ekman pumping drives a conversion of energy from APE to KE at small scales, and from KE to APE at large scales, even in the absence of a mean isopycnal slope. It is also shown that Ekman pumping affects the mean buoyancy by slightly weakening the stratification near the bottom boundary.

Large numbers of relative periodic orbits (RPOs) have been found recently in doubly periodic, two-dimensional Kolmogorov flow at moderate Reynolds numbers ${\textit{Re}} \in \{40, 100\}$. While these solutions lead to robust statistical reconstructions at the ${\textit{Re}}$ values where they were obtained, it is unclear how their dynamical importance changes with ${\textit{Re}}$. Arclength continuation on this library of solutions reveals that large numbers of RPOs quickly become dynamically irrelevant, reaching dissipation values either much larger or smaller than the values typical of the turbulent attractor at high ${\textit{Re}}$. The scaling of the high-dissipation RPOs is shown to be consistent with a direct connection to solutions of the unforced Euler equation, and is observed for a wide variety of states beyond the ‘unimodal’ solutions considered in previous work (Kim & Okamoto, Nonlinearity vol. 28, 2015, p. 3219). However, the weakly dissipative states have properties indicating a connection to exact solutions of a forced Euler equation. The dynamical irrelevance of many solutions leads to poor statistical reconstruction at higher ${\textit{Re}}$, raising serious questions for the future use of RPOs for estimating probability densities. Motivated by the Euler connection of some of our RPOs, we also show that many of these states can be well described by exact relative periodic solutions in a system of point vortices. The point vortex RPOs are converged via gradient-based optimisation of a scalar loss function which (i) matches the dynamics of the point vortices to the turbulent vortex cores and (ii) insists the point vortex evolution is itself time-periodic.

A deep-learning-based closure model to address energy loss in low-dimensional surrogate models based on proper-orthogonal-decomposition (POD) modes is introduced. Using a transformer-encoder block with an easy-attention mechanism, the model predicts the spatial probability density function of fluctuations not captured by the truncated POD modes. The methodology is demonstrated on the wake of the Windsor body at yaw angles of $\delta = [2.5^\circ ,5^\circ ,7.5^\circ ,10^\circ ,12.5^\circ ]$, with $\delta = 7.5^\circ$ as a test case, and in a realistic urban environment at wind directions of $\delta = [-45^\circ ,-22.5^\circ ,0^\circ ,22.5^\circ ,45^\circ ]$, with $\delta = 0^\circ$ as a test case. Key coherent modes are identified by clustering them based on dominant frequency dynamics using Hotelling’s $T^2$ on the spectral properties of temporal coefficients. These coherent modes account for nearly $60 \,\%$ and $75 \,\%$ of the total energy for the Windsor body and the urban environment, respectively. For each case, a common POD basis is created by concatenating coherent modes from training angles and orthonormalising the set without losing information. Transformers with different size on the attention layer, (64, 128 and 256), are trained to model the missing fluctuations in the Windsor body case. Larger attention sizes always improve predictions for the training set, but the transformer with an attention layer of size 256 slightly overshoots the fluctuation predictions in the Windsor body test set because they have lower intensity than in the training cases. A single transformer with an attention size of 256 is trained for the urban flow. In both cases, adding the predicted fluctuations close the energy gap between the reconstruction and the original flow field, improving predictions for energy, root-mean-square velocity fluctuations and instantaneous flow fields. For instance, in the Windsor body case, the deepest architecture reduces the mean energy error from $37 \,\%$ to $12 \,\%$ and decreases the Kullback–Leibler divergence of velocity distributions from ${\mathcal{D}}_{\mathcal{KL}}=0.2$ to below ${\mathcal{D}}_{\mathcal{KL}}=0.026$.

Compliant walls made from homogeneous viscoelastic materials may attenuate the amplification of Tollmien–Schlichting waves (TSWs) in a two-dimensional boundary-layer flow, but they also amplify travelling-wave flutter (TWF) instabilities at the interface between the fluid and the solid, which may lead to a premature laminar-to-turbulent transition. To mitigate the detrimental amplification of TWF, we propose to design compliant surfaces using phononic structures that aim at avoiding the propagation of elastic waves in the solid in the frequency range corresponding to the TWF. Thus, stiff inserts are periodically incorporated into the viscoelastic wall in order to create a band gap in the frequency spectrum of the purely solid modes. Fluid–structural resolvent analysis shows that a significant reduction in the amplification peak related to TWF is achieved while only marginal deterioration in the control of TSWs is observed. This observation suggests that the control of TSWs is still achieved by the overall compliance of the wall, while the periodic inserts inhibit the amplification of TWF. Bloch analysis is employed to discuss the propagation of elastic waves in the phononic surface to deduce design principles, accounting for the interaction with the flow.

The complex behaviour of air–liquid interfaces driven into Hele-Shaw channels at high speeds could arise from oscillatory dynamics; yet both the physical and dynamical mechanisms that lead to interfacial oscillations remain unclear. We extend the experiments by Couder et al. (1986, Phys. Rev. A, vol. 34, 5175) to present a systematic investigation of the dynamics that results when a small air bubble is placed at the tip of a steadily propagating air finger in a horizontal Hele-Shaw channel. The system can exhibit steady and oscillatory behaviours, and we show that these different behaviours each occur in well-defined regions of the phase space defined by flow rate and bubble size. For sufficiently large flow rates, periodic finger oscillations give way to disordered dynamics characterised by an irregular meandering of the finger’s tip. At fixed flow rate, the oscillations commence when the bubble size is increased sufficiently that the decreased curvature of the bubble tip in the horizontal plane matches that of the finger tip. This causes the axial pressure gradient along the bubble to vanish, thus rendering the bubble susceptible to lateral perturbations. Differing time scales for finger and bubble restoral allow sustained oscillations to develop in the finger–bubble system. The oscillations cease when the bubble is sufficiently large that it can act as the tip of a single finger. The disordered dynamics at high flow rates are consistent with the transient exploration of unstable periodic states, which suggests that similar dynamics may underlie disorder in viscous fingering.

An asymptotic model for the flow of a highly viscous film coating the interior of a slippery, flexible tube is developed and studied. The model is valid for the axisymmetric flow of moderately thick films, and accounts for tube flexibility, wall damping, longitudinal tension, slip length and strength of base flow due either to gravity or airflow. In the absence of base flow, linear stability analysis shows the existence of one unstable mode; the presence of base flow allows for multiple unstable modes arising due to the Plateau–Rayleigh instability and elastic instability, with stronger base flow reducing the maximum growth rate. Numerical solutions in the absence of base flow show that slip decreases the amplitude of wall deformations and can significantly decrease the time to plug formation in weakly flexible or strongly damped tubes. For falling films, the impact of model parameters on the critical thickness required for plug formation was analysed by studying turning points in families of travelling-wave solutions; this thickness decreases with slip, flexibility and tension, while damping had a non-monotonic impact on critical thickness. In contrast to model solutions in rigid tubes, for flexible tubes the critical thickness cannot be made arbitrarily large through simply increasing the strength of the base flow. For air-driven films, both slip and flexibility increase the rate of film transport along the tube.

Experiments have shown that ultrasound-stimulated microbubbles can translate through gel phantoms and tissues, leaving behind tunnel-like degraded regions. A computational model is used to examine the tunnelling mechanisms in a model material with well-defined properties. The high strain rates motivate the neglect of weak elasticity in favour of viscosity, which is taken to degrade above a strain threshold. The reference parameters are motivated by a 1 $\unicode{x03BC}$m diameter bubble in a polysaccharide gel tissue phantom. This is a reduced model and data are scarce, so close quantitative agreement is not expected, but tunnels matching observations do form at realistic rates, which provides validation sufficient to analyse potential mechanisms. Simulations of up to 100 acoustic cycles are used to track tunnelling over 10 bubble diameters, including a steady tunnelling phase during which tunnels extend each forcing cycle in two steps: strain degrades the tunnel front during the bubble expansion, and then the bubble is drawn further along the tunnel during its subsequent inertial collapse. Bubble collapse jetting is damaging, though it is only observed during a transient for some initial conditions. There is a threshold behaviour when the viscosity of the undamaged material changes the character of the inertial bubble oscillation. Apart from that, the tunnel growth rate is relatively insensitive to the high viscosity of the material. Higher excitation amplitudes and lower frequencies accelerate tunnelling. That acoustic radiation force, elasticity and bubble jetting are not required is a principal conclusion.

We investigate interactions between two like-signed vortices over either an isolated seamount or a basin (a depression in the bathymetry), using a quasi-geostrophic, two-layer model on the $f$-plane. When the vortex pair is centred over the seamount, the vortices are pushed together by the secondary flow generated in the bottom layer, facilitating their merger. Over a basin, the deep anomalies are much stronger and their interaction strains out the surface vortices. The results are supported by an analytical estimation of the initial potential vorticity anomalies in the lower layer and by analysis of the linear stability of a single vortex over the bathymetry. Similar phenomena are observed when the vortex pair is displaced from the bathymetric centre and when the initial vortices are initially compensated. Sub-deformation-scale vortices are less influenced by bathymetry than larger vortices. The results help explain asymmetries noted previously in turbulence simulations over bathymetry.

Pendant drops appear in many engineering applications, such as inkjet printing and optical tensiometry, and they have also been the subject of studies of droplet–particle interaction. While the hydrostatics of pendant drops has been studied extensively, the influence of external flow disturbances has received limited attention. This research aims to incorporate aerodynamic factors into the understanding of pendant drop behaviour. Employing a simplified model, an irrotational flow aligned with the drop’s axis is derived from a distribution of singularity elements within the drop. The drop’s equilibrium shape is then determined using a numerical model that couples the flow field with the Young–Laplace equation. The model’s predictions are compared to droplet images captured via high-speed shadowgraph in a vertical wind tunnel, showing good agreement with the experimentally observed shapes. Additionally, under certain flow conditions, the drop exhibits instability in the form of periodic pendulum-like motion. This instability was linked to two distinct critical drop heights, and the corresponding stability criterion was mathematically derived from the numerical model. Our theoretical and experimental findings provide the first quantitative description of the equilibrium shape and stability criterion of pendant drops under the influence of external flow.

If a body of inviscid fluid is disturbed, it will typically eject a jet of fluid. If the effects of gravity and surface tension are negligible, these jets travel in straight lines, with the tips approaching a constant velocity. Earlier works have concentrated upon jets which result from the occurrence of shocks or singularities in the fluid flow. In this paper, by contrast, we describe the simplest case, in two dimensions: an infinitely deep body of inviscid fluid, with no surface tension or gravitational forces acting, responds to a generic impulsive disturbance. We find that, contrary to some earlier suggestions, the jet has a hyperbolic profile (away from its tip and its base).

We investigate theoretically the breakup dynamics of an elasto-visco-plastic filament surrounded by an inert gas. The filament is initially placed between two coaxial disks, and the upper disk is suddenly pulled away, inducing deformation due to both constant stretching and capillary forces. We model the rheological response of the material with the Saramito–Herschel–Bulkley (SHB) model. Assuming axial symmetry, the mass and momentum balance equations, along with the constitutive equation, are solved using the finite element framework PEGAFEM-V, enhanced with adaptive mesh refinement with an underlying elliptic mesh generation algorithm. As the minimum radius decreases, the breakup dynamics accelerates significantly. We demonstrate that the evolution of the minimum radius, velocity and axial stress follow a power-law scaling, with the corresponding exponent depending on the SHB shear-thinning parameter, $n$. The scaling exponents obtained from our axisymmetric simulations under creeping flow are verified through asymptotic analysis of the slender filament equations. Our findings reveal three distinct breakup regimes: (a) elasto-plastic, (b) elasto-plasto-capillary, both with finite-time breakup for $n\lt 1$, and (c) elasto-plasto-capillary with no finite-time breakup for $n=1$. We show that self-similar solutions close to filament breakup can be achieved by appropriate rescaling of length, velocity and stress. Notably, the effect of the yield stress becomes negligible in the late stages of breakup due to the local dominance of high elastic stresses. Moreover, the scaling exponents are independent of elasticity, resembling the breakup behaviour of finite extensible viscoelastic materials.

We developed a numerical method to investigate the effects of flow properties and phase transition between a gas and a liquid on sloshing-induced impact pressures acting on the walls of a partially filled tank. The conservation equations of mass, momentum and energy, as well as a transport equation for the volume fraction, were solved by considering flow compressibility, surface tension and phase transition. We modelled the phase transition by employing a mass transfer model, and validated our numerical method against experimental data. We investigated the effects of flow compressibility and density ratio between gas and liquid, representing a range similar to that of natural gas and hydrogen. We examined the effects of phase transition on sloshing-induced impact loads caused by a single-impact wave with gas pockets. Compressibility, density ratio and phase transition significantly affected the flow of the liquid–gas interface in the tank and, consequently, the impact pressure. The gas compressibility, caused by a single-wave impact with gas pockets, reduced the impact pressures significantly. Although the influence of density ratio on impact pressures is often emphasised, we demonstrated that, for impacts with gas pockets, the gas density was decisive and not the density ratio. With increasing gas density, the shape of the liquid–gas interface changed, and the pressure peak decreased. For the cases investigated, the viscosity of the liquid phase hardly influenced the impact pressures. Furthermore, the phase change during condensation considerably reduced the impact pressure peak. The pressure fluctuations after the first impact were strongly damped due to the vaporisation process.

In this paper, a phase-change model based on a geometric volume-of-fluid (VOF) framework is extended to simulate nucleate boiling with a resolved microlayer and conjugate heat transfer. Heat conduction in both the fluid and solid domains is simultaneously solved, with interfacial heat-transfer resistance (IHTR) imposed. The present model is implemented in the open-source software Basilisk with adaptive mesh refinement (AMR), which significantly improves computational efficiency. However, the approximate projection method required for AMR introduces strong oscillations within the microlayer due to intense heat and mass transfer. This issue is addressed using a ghost fluid method, allowing nucleate boiling experiments to be successfully replicated. Compared with previous literature studies, the computational cost is reduced by three orders of magnitude. We investigated the impact of contact angle on nucleate boiling through direct numerical simulation (DNS). The results show that the contact angle primarily influences the bubble growth by altering the hydrodynamic behaviour within the microlayer, rather than the thermal effect. An increase in contact angle enhances contact line mobility, resulting in a slower bubble growth, while maintaining an approximately constant total average mass flux. Furthermore, the sensitivity of bubble dynamics to the contact angle diminishes as the angle decreases. Finally, a complete bubble cycle from nucleation to detachment is simulated, which, to our knowledge, has not been reported in the open literature. Reasonable agreement with experimental data is achieved, enabling key factors affecting nucleate boiling simulations in the microlayer regime to be identified, which were previously obscured by limited simulation time.

This study considers the global instability of unidirectional flows through single, and double, bifurcation models using linear stability and direct numerical simulation (DNS). The motivation is respiratory flows, so we consider flow in both directions, through two geometries. We identify conditions (quantified by the Reynolds number, ${Re}=U^*D/\nu$, where $U^*$ is the peak centreline velocity, $D$ is the primary pipe diameter and $\nu$ is the kinematic viscosity) where temporal fluctuations occur using DNS. We calculate the linear stability of the steady flows, identifying the critical Reynolds number and leading unstable modes. For flows from single to double pipe, the critical Reynolds number is dependent on the number of bifurcations in the domain, but the mode structures are similar, with growth observed in regions dominated by longitudinal vortices formed by the centrifugal imbalance of flows passing through curved bifurcations. Flows in the opposite direction, from double to single pipe, also depend on the number of bifurcations in the domain. The flow through the double-bifurcation case undergoes two spatial symmetry-breaking bifurcations, altering the mode structure and critical Reynolds number. In all cases, the critical Reynolds number closely matches with temporal fluctuations observed from DNS, suggesting transition is the result of a linear instability, similar to other curved geometries like toroidal and helical pipes. We compare the frequencies of the modes with the frequencies observed from DNS, finding a close match during both initial and saturated flows. These results are important for understanding respiratory flows where turbulent mixing and streaming contribute to gas transport.

When a water wave group encounters a floating body, it forces the body into motion; this motion radiates waves that modify the wave group. This study considers a floating body in the form of a two-dimensional (2-D) rectangular block constrained to heaving motion. The focus is on how the 2-D block modifies infragravity (IG) waves, a type of nonlinear low-frequency wave in the wave group. The IG waves transmitted beyond the block comprise two types: (i) bound IG waves generated by nonlinear interactions of first-order carrier waves, and (ii) free IG waves released due to discontinuities in flow potential created by the block. A systematic parameter sweep reveals that, when heaving motion is allowed, the transmitted IG waves differ significantly from those of stationary blocks. In some cases, heaving motion enables attenuation of the total transmitted IG waves, while stationary blocks cannot achieve similar effects. Only small-sized blocks are considered; they are ‘small’ compared with the IG wavelengths. The findings are relevant to dual-purpose wave energy converters designed for energy generation and coastal protection, floating breakwaters and other small-sized floating structures such as ships and some icebergs: the heaving motion of these objects may modify IG waves, thereby influencing harbour resonance, near-shore currents, beach erosion, wave forcing on ice shelves and coastal inundation.

In this work, we derive higher-order transport equations starting from the Boltzmann equation using a second-order accurate distribution function within the 13-moment framework. The equations are shown to be unconditionally linearly stable and consistent with Onsager’s symmetry principle. We also show that the equations comply with the second law of thermodynamics by establishing the non-negativity of the bulk entropy generation rate using the linearised form of the proposed equations. The force-driven Poiseuille flow problem, a standard benchmark problem, is selected to establish the validity of the equations. A complete analytical solution for this problem is proposed and compared against the Navier–Stokes, regularised 13, Grad 13 solutions and direct simulation Monte Carlo data. The proposed solution captures key rarefaction effects, including the Knudsen layer, non-uniform bimodal pressure profile, non-Fourier heat flux and the characteristic temperature dip at the centre. The analytical solution for the field variables indicates that the equations outperform the existing models in the slip- and transition-flow regimes for the problem considered. These satisfactory results point to the accuracy and applicability of the proposed equations, and the equations hold significant promise for rarefied gas dynamics at large Knudsen numbers.