The force on a spherical particle moving arbitrarily in a fairly general class of unsteady potential flows is calculated. It is found that the force, which can be expressed as the gradient of a potential, takes the form of an infinite series of progressively higher order in the ratio of the sphere’s radius to the scales of the surrounding flow. The first few terms conform with the known form usually referred to as ‘added mass force’ but, when the remaining terms are non-negligible, this concept becomes less relevant. Thus, unlike Faxèn’s extension of Stokes’s drag law, it proves impossible to generalise the idea of added mass to particles that are not much smaller than the flow scales. The kinetic energy of the fluid in excess of that which it would have in the absence of the sphere is also calculated when the flows considered are unbounded.

We investigate the transitional flow regimes arising from the interaction between buoyancy and shear in Rayleigh–Bénard–Poiseuille (RBP) flows, considering both large and small domains. The transition boundaries between the bistable system consisting of spiral defect chaos (SDC) and ideal straight rolls (ISRs) in Rayleigh–Bénard convection, and subcritical turbulence in plane Poiseuille flows are not known. Using direct numerical simulations in a large spatial domain over a range of Rayleigh numbers, $Ra \in [0, 10000]$, Reynolds numbers, $\textit{Re} \in [0, 2000]$ and unit Prandtl number, we identify five distinct regimes: (i) bistable SDC and ISRs; (ii) ISRs; (iii) wavy rolls; (iv) intermittent rolls; and (v) shear-driven turbulence. The newly identified intermittent rolls state features longitudinal rolls that decay towards the laminar state before regenerating. In the turbulent regime, longitudinal rolls may coexist with turbulent–laminar bands, highlighting the role of longitudinal rolls in transitional RBP flows. To this end, we examine the unstable manifold of longitudinal rolls in a small domain, integrating along which led to turbulence. This turbulence occur transiently, decaying towards the unstable laminar base state where the longitudinal rolls can be excited again, forming a quasi-cyclic process referred to as the thermally assisted sustaining process (TASP). We further investigate the behaviour of TASP as $\textit{Re}$ and $Ra$ are varied, revealing a stable periodic orbit around the longitudinal roll and the laminar state, and a pathway towards turbulence above a certain $\textit{Re}$ threshold. Finally, we provide a state space sketch of the dynamical processes, emphasising the role of longitudinal rolls in transitional RBP in small domains, and discuss the potential connections to large domains.

Active particles exhibit complex transport dynamics in flows through confined geometries such as channels or pores. In this work, we employ a generalised Taylor dispersion (GTD) theory to study the long-time dispersion behaviour of active Brownian particles in an oscillatory Poiseuille flow within a planar channel. We quantify the time-averaged longitudinal dispersion coefficient as a function of the flow speed, flow oscillation frequency and particle activity. In the weak-activity limit, asymptotic analysis shows that activity can either enhance or hinder the dispersion compared with the passive case. For arbitrary activity levels, we numerically solve the GTD equations and validate the results with Brownian dynamics simulations. We show that the dispersion coefficient can vary non-monotonically with both the flow speed and particle activity. Furthermore, the dispersion coefficient shows an oscillatory behaviour as a function of the flow oscillation frequency, exhibiting distinct minima and maxima at different frequencies. The observed oscillatory dispersion results from the interplay between self-propulsion and oscillatory flow advection – a coupling absent in passive or steady systems. Our results show that time-dependent flows can be used to tune the dispersion of active particles in confinement.

We investigate the emergence of an anomalous solutocapillary instability in an isothermal nanofluid layer with a non-deformable liquid–gas interface. A model of the equation of state for the colloidal suspension is presented. The surface tension exhibits non-monotonic variation with nanoparticle concentration due to nanoparticle surface energetics. In what follows, we consider nanoparticle interfacial kinetics and express the dynamics of surface concentration via the spatio-temporal evolution equation. We analyse the linear stability around the quiescent base state using normal modes and deduce the linear eigenvalue problem to determine the growth rates of these modes. The analytical solution for the monotonic solutocapillary instability is found. Surprisingly, the system displays the onset of an anomalous short-wave solutocapillary instability due to an increase in surface tension with the particle concentration.

We give evidence of non-modal amplification mechanisms driven by swirl intensity from a bi-global linear analysis of a cold swirling flow representative of a premixed swirl burner: non-uniform, compressible, turbulent, enclosed and subject to vortex breakdown passed the expansion. The monolithic computational approach embeds a realistic axisymmetric swirler model in the computational domain. The amplification mechanisms are identified by stability and resolvent analysis under variations of the length of the annular duct section and combustion chamber, the swirl intensity and the swirler position. While the spectrum is affected by changes in the length only, the gain of the resolvent strongly depends on the swirl intensity. The results suggest an acoustically dominated amplification in the combustion chamber and a non-modal hydrodynamic-dominated process driven by the swirl intensity. Inertial waves carrying swirl fluctuations play a key role in the latter. The results are complemented by a resolvent sensitivity analysis that identifies the tip of the inner recirculation region and the surrounding shear layer as a wavemaker region that drives at high swirl numbers the non-modal amplification. The sensitivity of that region also enables the transfer of azimuthal momentum perturbations to axial momentum, hence activating a longitudinal acoustic resonance from azimuthal fluctuations.

Wall-pressure fluctuations beneath turbulent boundary layers (BLs) drive noise and structural fatigue through interactions between fluid and structural modes. Conventional predictive models for the spectrum – such as the widely accepted Goody model (2004 AIAA J., vol. 42 (9), pp. 1788–1794) – fail to capture the energetic growth in the low-frequency range that occurs at high Reynolds number, while at the same time over-predicting the variance. To address these shortcomings, two semi-empirical models are proposed for the wall-pressure spectrum in canonical turbulent BLs, pipes and channels for friction Reynolds numbers $\delta ^+$ ranging from 180 to 47 000. Consistent with the approach outlined modelling the streamwise Reynolds stress in the recent work of Gustenyov et al. (2025 J. Fluid Mech., vol. 1016, A23), the models are based on consideration of two spectral components that represent the contributions to the wall-pressure fluctuations from inner-scale motions and outer-scale motions. The first model expresses the pre-multiplied spectrum as the sum of two overlapping log-normal components: an inner-scaled term that is $\delta ^+$-invariant and an outer-scaled term whose amplitude broadens smoothly with $\delta ^+$. Calibrated against large-eddy simulations, direct numerical simulations and recent high-$\delta ^+$ pipe data, it reproduces the inner-scaled peak and the emergence of an outer-scaled peak at large $\delta ^+$. The second model, developed around newly available pipe data, uses theoretical arguments to prescribe the spectral shapes of the inner and outer components. Embedding the $\delta ^+$-dependence in smooth asymptotic functions yields a formulation that varies continuously with $\delta ^+$ and generalises beyond the calibration range. Both models capture the full spectrum and recover the observed logarithmic growth of its variance, providing a compact, physics-informed empirical representation for more accurate engineering predictions of wall-pressure fluctuations.

This work experimentally investigates Richtmyer–Meshkov (RM) turbulence driven by a cylindrical converging shock using time-resolved planar laser-induced fluorescence. An automatically retractable plate is developed to generate membraneless yet sharp interfaces characterised by random short-wavelength perturbations and controllable long-wavelength components. Five initial interfaces are examined: one with random short-wavelength perturbations, and four with these random perturbations superimposed with single-mode long-wavelength perturbations of controlled amplitude and wavenumber. The shocked interface in the converging configuration exhibits strongly unsteady motion: it initially moves inwards uniformly, then decelerates, moves outwards following reshock, and finally decelerates again with noticeable oscillations. The interface initially develops with a well-defined morphology, but quickly transitions to turbulent mixing after reshock. Both reshock and Rayleigh–Taylor instability, unique to converging RM flows, significantly influence the mixing layer evolution. The mixing width exhibits significantly higher post-reshock growth rates compared with the planar counterpart. Scalar mixedness analysis indicates that the random-perturbation case achieves significantly higher homogenisation efficiency than single-mode cases, whereas the mean scalar dissipation rate follows a similar temporal pattern regardless of initial morphology. The initial perturbation spectrum strongly influences the timing of turbulent transition: the high-wavenumber single-mode case reaches the empirical threshold earliest, followed by the random-perturbation case, while the low-wavenumber single-mode cases exhibit substantially delayed or incomplete transition. Scalar energy spectra further highlight that initial perturbations critically affect the efficiency of turbulent cascade and the small-scale energy distribution.

Richtmyer–Meshkov instability (RMI) at quasi-single-mode interfaces subjected to strong shocks with Mach number exceeding 3.0 is investigated through shock-tube experiments. To reveal the influence of higher-order initial modes, one single-mode and four quasi-single-mode interfaces with varying modal compositions are examined. The Richtmyer theory is experimentally verified for the first time to accurately capture the single-mode interface evolution from start-up to the linear stage. In contrast, it fails for quasi-single-mode scenarios, highlighting the significant effect of higher-order modes. By incorporating the influence of higher-order modes via linear superposition, a linear model for quasi-single-mode interface evolution is proposed, whose validation indicates negligible modal coupling in early evolution. For the nonlinear period, a representative model for weak-shock-driven RMI at a single-mode interface performs poorly, as it does not consider the influence of higher-order modes and key mechanisms such as shock proximity, secondary compression and spike acceleration. Based on the present findings, an empirical nonlinear model with favourable predictive capability is developed. Furthermore, by matching the new linear and nonlinear models, a complete description of the amplitude evolution of single-mode and quasi-single-mode interfaces from start-up to nonlinear stages is achieved, offering new insight into modelling strong-shock-driven RMI.

We perform direct numerical simulations of flows over finite-aspect-ratio rotating circular cylinders at a Reynolds number of 150 over a range of aspect ratios (${\rm AR}=2{-}12$) and rotation rates ($\alpha =0{-}5$), aiming to reveal the free-end effects on wake dynamics and aerodynamic performance. As a direct consequence of lift generation, a pair of counter-rotating tip vortices form at the free ends. At low rotation rates, the finite rotating cylinder behaves like a typical bluff body that generates unsteady vortex shedding with three-dimensional modal structures. Such unsteady flows can be stabilised not only by increasing the rotation rate, which weakens the free shear layer, but also by decreasing the aspect ratio which enhances the tip-vortex-induced downwash. A further increase of $\alpha$ triggers the onset of unsteadiness in the tip vortices. At still higher rotation rates, C-shaped Taylor-like vortices bounded on the cylinder surface emerge from the free ends and migrate towards the midspan due to self-induced velocity from vortex–wall interaction. With increasing $\alpha$, the free-end effects penetrate to the inboard span, leading to reduced lift and elevated drag compared with two-dimensional flows. The three-dimensional end effects can be effectively suppressed by adding end plates, which position the tip vortices away from the cylinder, thereby significantly improving aerodynamic performance. This study reveals the mechanisms for three-dimensional wake formation under the influence of the free ends of finite rotating cylinders. The insights obtained here serve as a stepping stone for understanding complex high-$ \textit{Re}$ flows relevant to industrial applications.

This study presents a systematic investigation of hydrodynamic forces on a stationary circular cylinder inside relatively wide and deep trapezoidal trenches in steady flows, representing subsea power cables laid in seabed valleys or artificial trenches, with particular emphasis on the role of Kelvin–Helmholtz (K–H) instability. Using high-fidelity three-dimensional (3-D) implicit large-eddy simulation (iLES), the influences of trench geometry and the incoming flows on hydrodynamic forces were examined. The parametric space includes the trench-width-to-cylinder-diameter ratio ($ W^{*}$ $\leq$ 20), trench-depth-to-cylinder-diameter ratio ($H^{*} \leq 5$), trench side slope ($15^{\circ}\leq \theta \leq 60^{\circ}$) and the streamwise offset of the cylinder centre from the trench centreline (${L}_{p}^{*}$). The large-scale cavity-type flows generated by trench geometry and K–H shear-layer dynamics originating at the leading edge of the trench are found to be the dominant mechanisms affecting hydrodynamic forces on the cylinder. Narrow, deep and steep-sided trenches are shown to provide a sheltering effect, reducing forces on the cylinder; whereas wide, shallow trenches promote the generation of strong K–H instabilities that interact directly with the cylinder, leading to periodic force fluctuations. Notably, when the cylinder is positioned downstream of the shear-layer reattachment point in a wide, shallow trench, the mean drag and/or lift forces can exceed those experienced over a flat seabed, accompanied by substantial fluctuations. Increasing Reynolds number (Re) from 500 to 3900, as defined based on the diameter of the cylinder, enhances fluctuations of hydrodynamic forces, primarily due to the upstream migration of the onset of K–H instability and the intensified interactions of shed vortices with the cylinder within the trench. A hydrodynamic regime map, constructed from mean force reduction factors and peak fluctuation intensities, is proposed to classify the flow into four distinct regimes: no interaction, transitional, interaction and strong interaction. These findings offer new physical insights and provide practical guidance for evaluating hydrodynamic responses on unburied subsea cables in complex seabed topographies.

Zonal winds on Jovian planets play an important role in governing the cloud dynamics, transport of momentum, scalars and weather patterns. Therefore, it is crucial to understand the evolution of zonal flows and their sustainability. Based on studies in two-dimensional $\beta$-plane set-ups, zonal flow is believed to be forced at the intermediate scale via baroclinic instabilities, and the inverse cascade leads to the transfer of energy to large scales. However, whether such a process exists in three-dimensional deep convection systems remains an open and challenging question. To explore a possible answer, we perform large-eddy simulations at Rayleigh and Ekman numbers in the spans $10^7 {-} 10^{12}$ and $10^{-3}{-}10^{-8}$, respectively, corresponding to the inverse of the convective Rossby number, $1/Ro_c$, ranging from $0.1685$ to $168.52$, in a horizontally rotating Rayleigh–Bénard convection set-up. We find the emergence of mean flow at the expense of small-scale turbulence for $1/Ro_c = 1.68522$, $16.852$ and $168.52$. The turbulent kinetic energy budget analysis shows negative turbulent production in zonal flows, implying an energy transfer from the fluctuating velocity fields to the mean flow. We further quantify this energy transfer in spectral space using the kinetic energy spectra and the energy flux, and conclude that the energy deposited at small scales owing to the work done by buoyancy is transferred to large scales via upscale energy transfer, thus corroborating the emanation of a strong mean flow from chaos.

We examine theoretically the flow interactions and forward flight dynamics of tandem or in-line flapping wings. Two wings are driven vertically with prescribed heaving motions, and the horizontal propulsion speeds and positions are dynamically selected through aero- or hydro-dynamic interactions. Our simulations employ an improved vortex-sheet method to solve for the locomotion of the pair within the collective flow field, and we identify ‘schooling states’ in which the wings travel together with nearly constant separation. Multiple terminal configurations are achieved by varying the initial conditions, and the emergent separations are approximately integer multiples of the wavelength traced out by each wing. We explain the stability of these states by perturbing the follower and mapping out an effective potential for its position in the leader’s wake. Each equilibrium position is stabilised since smaller separations are associated with in-phase follower-wake motions that constructively reinforce the flow but lead to decreased thrust on the follower; larger separations are associated with antagonistic follower-wake motions, increased thrust and a weakened collective wake. The equilibria and their stability are also corroborated by a linearised theory for the motion of the leader, the wake it produces and its effect on the follower. We also consider a weakly flapping follower driven with lower heaving amplitude than the leader. We identify ‘keep-up’ conditions for which the wings may still ‘school’ together despite their dissimilar kinematics, with the ‘freeloading’ follower passively assuming a favourable position within the wake that permits it to travel significantly faster than it would in isolation.

The behaviour of internal waves propagating in a background shear flow is studied in the case where the direction of shear is orthogonal to gravity. Ray-tracing theory is used to predict properties of the wave state at locations where instability occurs. Local wave energy growth is found to result from two distinct mechanisms: an increase in wave steepness due to refraction by the shear or an increase in streamwise velocity perturbations due to wave advection of the background flow. Based on the initial conditions, a dimensionless perturbation energy ratio $F$ is constructed to predict the relative importance of these two mechanisms in facilitating wave breaking. When $F$ is small and waves become locally steep, perturbation kinetic and potential energy remain approximately equipartitioned and subsequent instabilities are expected to develop due to a combination of shear and convection. On the other hand, as $F$ increases, kinetic energy dominates and wave advection of momentum may instead cause breaking to become increasingly driven by enhanced vertical shear. To test these predictions, fully nonlinear direct numerical simulations are conducted, spanning a range of wave-breaking dynamics. Good qualitative agreement with the theory is found despite substantial departures from the underlying assumptions. Wave breaking leads to significant turbulent dissipation, which in some cases greatly exceeds the initial wave energy. Momentum and energy transfers between the wave, background flow and turbulence are found to be sensitive to the dynamics of breaking, as are the mixing properties.