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.

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.

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.

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.

Laminar–turbulent transition in shear flow is complicated and follows many possible routes. In this study, we seek to examine a scenario based on three-dimensional (3-D) waves (Jiang et al., 2020, J. Fluid Mech., vol. 890, A11) in compressible mixing layers, and elucidate the role of 3-D waves in generating streamwise vorticity. The Eulerian–Lagrangian coupled method is used to track the evolution of flow structures. Qualitative evidence shows that localised 3-D waves travel coherently with vortex structures at the early transition stage, which is consistent with the behaviours of 3-D waves in boundary layer transitions. To examine the local flow events surrounding 3-D waves and investigate the cause and effect relationships inherent in wave–vortex interaction, the finite-time Lyapunov exponent and components of the strain rate tensor are integrated into evolving Lagrangian material surfaces. The formation of high-shear layers in the flanks of the 3-D waves is observed, driven by fluid ejection and sweep motions induced by the amplification of 3-D waves. The $\Lambda$-shaped vortices are found born in the vicinity of high-shear regions and then stretched into hairpin-shaped vortices farther downstream. Statistical findings reveal that streamwise vorticity develops concurrently with the significant growth of the oblique mode, while the normal motion of wave structures induces a high strain rate layer in the surrounding region. In addition, conditional statistics underscore the significance of high shear in enstrophy generation. Finally, a conceptual model is proposed to depict the evolution of coherent structures based on the relationship among the 3-D waves, high-shear/strain layers, and $\varLambda$-vortices, providing insights into their collective dynamics within transitional mixing layers.

Finite-amplitude spiral vortex flows are obtained numerically for the Taylor–Couette system in the narrow limit of the gap between two concentric rotating cylinders. These spiral vortex flows bifurcate from circular Couette flow before axisymmetric Taylor vortex flow sets in when the ratio $\mu$ of the angular velocities of the outer to the inner cylinder is less than −0.78, consistent with the results of linear stability analysis by Krueger et al. (J. Fluid Mech., vol. 24, 1966, pp. 521–538), while the boundary of existence of spiral vortex flows is determined not by the linear critical point, but by the saddle-node point of the subcritical spiral vortex flow branch for $\mu \lessapprox -0.75$, when the axial wavenumber $\beta =2.0$. It is found that the nonlinear spiral vortex flows exhibit the mean flow in the axial direction as well as in the azimuthal direction, and that the profiles of both mean-flow components are asymmetric about the centre plane between the gap.

In this work the fascinating dynamics of a two-layered channel flow characterised by the dispersion in composite media within its layers is investigated in depth. The top layer comprises of a fluid zone that allows the fluid to travel along its surface easily (with relatively higher velocity), while the bottom layer is packed with porous media. The primary objective of this research is to do an in-depth investigation of the complex two-dimensional concentration distribution of a passive solute discharged from the inflow region. A multi-scale perturbation analysis approach has been implemented to address the system’s inherent complexity. This accurate determination of the dispersion coefficient, mean concentration distribution and two-dimensional concentration distribution is accomplished deftly using Mei’s homogenisation approach up to second-order approximation, which satisfactorily capture the minor variations in the solute dynamics also. The influence of various flow and porous media elements on these basic parameters is thoroughly investigated, expanding our comprehension of the complex interaction between flow dynamics and porous media’s properties. The effect of Darcy number and the ratio of two viscosities ($M$) on the dispersion coefficient depends on the height of the porous layer. As the Péclet number ratio increases, the dispersion coefficient experiences a concurrent increase, resulting in a decline in the concentration peak. The results of the analytical studies have also been compared with those results obtained using a purely computational method to establish the validity of our studies. Both the sets of results show quite good agreement with each other. In this study, alternate flow models have been used for the porous region, and the outcomes are compared to determine which approach yields more suitable results under different conditions.

The paper discusses the stochastic dynamics of the vortex shedding process in the presence of external harmonic excitation and coloured multiplicative noise. The situation is encountered in a turbulent practical combustor experiencing combustion instability. Acoustic feedback and turbulent flow are imitated by the harmonic and stochastic excitations, respectively. The Ornstein–Uhlenbeck process is used to generate the noise. A low-order model for vortex shedding is used. The Fokker–Planck framework is used to obtain the evolution of the probability density function of the shedding time period. Stochastic lock-in and resonance characteristics are studied for various parameters associated with the harmonic (amplitude, frequency) and noise (amplitude, correlation time, multiplicative noise factor) excitations. We observed that: (i) the stochastic lock-in (s-lock-in) boundary strongly depends on the noise correlation time; (ii) the parameter sites for s-lock-in can be approximately identified from the noise-induced shedding statistics; and (iii) stochastic resonance is significant for some intermediate correlation times. The effects of the above-mentioned observations are discussed in the context of combustion instability.

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 ${\mathcal{D}}_{\mathcal{KL}}=0.026$.

This paper explores decaying turbulence beneath surface waves that is initially isotropic and shear free. We start by presenting phenomenology revealed by wave-averaged numerical simulations: an accumulation of angular momentum in coherent vortices perpendicular to the direction of wave propagation, suppression of kinetic energy dissipation and the development of depth-alternating jets. We interpret these features through an analogy with rotating turbulence (Holm 1996 Physica D. 98, 415–441), wherein the curl of the Stokes drift, ${\boldsymbol{\nabla}} \times {\boldsymbol{u^{S}}}$, takes on the role of the background vorticity (for example, $(f_0 + \beta y) {\boldsymbol{\hat{z}}}$ on the beta plane). We pursue this thread further by showing that a two-equation model proposed by Bardina et al. (1985 J. Fluid Mech. 154, 321–336) for rotating turbulence reproduces the simulated evolution of volume-integrated kinetic energy. This success of the two-equation model – which explicitly parametrises wave-driven suppression of kinetic energy dissipation – carries implications for modelling turbulent mixing in the ocean surface boundary layer. We conclude with a discussion about a wave-averaged analogue of the Rossby number appearing in the two-equation model, which we term the ‘pseudovorticity number’ after the pseudovorticity ${\boldsymbol{\nabla }} \times {\boldsymbol{u}}^S$. The pseudovorticity number is related to the Langmuir number in an integral sense.

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.