This paper is devoted to revealing the effects of swirling flows with radially dependent velocity profiles on thermoacoustic instability. By reformulating the three-dimensional linearized Euler equations in cylindrical coordinates under standing-wave assumptions according to inlet/outlet boundary reflections, and integrating flame response dynamics, we develop a dispersion relation framework for thermoacoustic instability analysis. In so doing, the model generalizes prior network-based approaches for thermoacoustic instabilities (with axial and circumferential flow) to incorporate radial velocity gradients. Validation against analytical and numerical solutions for benchmark cases spanning thermoacoustic instabilities and aeroacoustic phenomena demonstrates quantitative agreement across configurations. Subsequent parametric studies further indicate that both radially dependent azimuthal and axial velocity components exert a considerable influence on the prediction of azimuthal thermoacoustic instability in an annular duct. This finding suggests that the assumption of uniform velocities in existing models may lead to inaccurate estimations of instability. Additionally, acoustic energy analysis indicates that axial flow components (perpendicular to inlet/outlet cross-sections) exhibit higher acoustic energy efflux at the combustor outlet than the circumferential components of swirling flows. Meanwhile, in comparison with burner-induced acoustic energy variations at the combustor inlet, an increase in the circumferential flow component reduces acoustic energy transmission at the combustor outlet for counter-propagating waves while amplifying it for copropagating waves. These effects are further enhanced by a stronger axial component of swirling flows. Overall, the proposed framework provides a foundational tool for elucidating thermoacoustic mechanisms and advancing instability mitigation strategies in a swirling flow configuration within confined spaces.

Mean strain rates can arise in fluids due to geometric deformation, or from bulk compression/expansion as from implosions/explosions. For interfacial instabilities, such as the Richtmyer–Meshkov instability (RMI), and the resulting turbulent mixing layers, the effect of strain depends on the direction of application. To analyse the influence of transverse strain rates, which is in the direction orthogonal to the amplitude or mixing layer growth, simulations are conducted in a Cartesian geometry with a moving mesh to control the strain application. Two regimes are analysed under the application of transverse strain rates. In the linear regime, a linearised potential flow model and supporting simulations demonstrate that transverse compression amplifies the instability growth. In contrast, simulations of the RMI-induced turbulent mixing layer show a decrease in the mixing layer width under transverse compression. The turbulent flow deviates from the self-similar state that is observed in the absence of strain, due to shear production and a modified turbulent length scale. The change in turbulent length scale causes a change in the dissipation rate, altering the evolution of the mixing layer. Predictive models for the mixing layer width and the domain-integrated turbulent kinetic energy are presented, which require scaling the drag/dissipation terms by the inverse of the transverse expansion factor to align with simulation results.

We investigate the instability of precession-driven flows in a stably stratified and rotating spherical shell using direct numerical simulations. Our results show that stable stratification can make precessional flows more unstable compared with the neutrally stratified fluid, when the Brunt–Väisälä frequency in the bulk is comparable to the rotation frequency. The instability arises from triadic resonances between the basic precessional flow and a pair of gravito-inertial waves. The excitation of gravito-inertial waves facilitates the angular momentum transport in the fluid interior, resulting in prominent differential rotation in stably stratified precessing fluids. Our numerical simulations suggest that mechanical forcings, such as precession, are possible to sustain complex flows and lead to the angular momentum transport in planetary fluid interiors, even if they are thermally stable after long-term cooling.

Taylor dispersion of a solute in a pulsatile flow of a viscoelastic fluid, whose constitutive equation follows the Maxwell model, through an eccentric annulus is investigated in this work. To determine the effective dispersion coefficient, $\mathscr{D}_{\textit{eff}}$, we have used the multiple-scale analysis in conjunction with the homogenization method. The governing equation describing this dispersive phenomenon for solute concentration is the advection-diffusion equation, which depends on the velocity profile. Therefore, the momentum equation must be solved in advance. A hyperbolic partial differential equation in a bipolar coordinate system was derived by combining the Cauchy momentum equation with Maxwell’s constitutive equation. Parameters such as the Womersley number, ${\textit{Wo}}$, and the Deborah number, ${\textit{De}}$, control the time-dependent flow and viscoelasticity, respectively. For low Womersley numbers, i.e. for low frequencies, an increase in the Deborah number, the eccentricity, $\phi$, and gap width, $\gamma$, leads to an enhancement of the effective dispersion coefficient. For instance, a fluid with ${\textit{De}} = 5$ could increase $\mathscr{D}_{\textit{eff}}$ by two orders of magnitude compared with a Newtonian fluid with the same settings ($\phi = 0.3$ and ${\textit{Wo}} = 0.1$). However, this enhancement due to the viscoelastic effect is only significant at low frequencies. An advection-diffusion equation for the mean concentration in the cross-section was also derived and evaluated in the same low-frequency limit. It was concluded that pulsatile flow maximises the axial dispersion compared with steady and purely oscillatory flows.

The dynamics of a liquid metal slug driven by electromagnetic induction under an unsteady magnetic field are investigated through experiments and numerical simulations. When a Galinstan slug is subjected to a rotating magnetic field in a circular container filled with an electrolyte solution, it exhibits regular circular revolutions along the circumferential edge of the container. To reveal the spatiotemporal distribution of the electromagnetic field within the slug and the temporal profile of the Lorentz force acting on the slug, we develop a numerical framework that fully resolves the coupled transient phenomena in the multi-physics and multi-phase system. The periodic magnetic field induces locally intensified eddy currents within the slug, which interact with the magnetic field to generate a pulse-like Lorentz force per magnet rotation cycle, eventually promoting the revolving motion of the slug. The maximum magnitude of the Lorentz force acting on the slug increases with the rotational speed of the permanent magnet, and the duration of the strong Lorentz force within the magnet rotation cycle increases with the mass of the slug. Based on the energy balance, a scaling relation that characterises the motion of the slug is developed. Experimental and numerical comparisons demonstrate that the proposed scaling relation predicts the angular velocity of the slug with reasonable accuracy. Our findings highlight a strategy for the remote manipulation of liquid metals, offering insights into soft actuation.

The rate at which weakly soluble gases transfer through natural air–water interfaces can be difficult to model because the transfer velocity depends on complex multi-scale dynamics at or near the interfaces. The impact of counter-rotating streamwise vortices, which occur in wind-driven water bodies and open channel flows, on interfacial gas transfer is not well understood. Laboratory studies were conducted in a wide, recirculating, open channel flume to quantify the impact of said vortices on gas transfer velocity. The counter-rotating streamwise vortices were stabilised using fixed longitudinal bed bars. Cases with bed bars were compared to cases without bed bars at three flow velocities (with depth-based Reynolds numbers from $1.7\times 10^4$ to $5.8\times 10^4$). Cases with bars on average exhibited 9–15 % faster gas transfer, 42–100 % more surface turbulent kinetic energy, and 20–50 % faster key turbulence time scales, likely due to enhanced shear and vertical transport of subsurface turbulence. Turbulence measurements demonstrate that the presence of the longitudinal bed bars leads to significant lateral heterogeneity in gas transfer.

Recent molecular-level simulations suggest that slip at solid–liquid interfaces can depend on shear. This work integrates molecular dynamics (MD) and direct numerical simulations (DNS) to quantify how shear-dependent slip modifies near-wall turbulence in wall-bounded flows. The MD is used to characterise how the slip length depends on wall shear stress across a range of solid–liquid affinities, revealing a threshold-like, bimodal response: the slip length is approximately constant at low and high stresses, with a sharp transition near a slip-activation threshold. This MD-derived relation is then implemented as a wall boundary condition in DNS of turbulent channel flow at friction Reynolds numbers 180, 400 and 1000, using five threshold values to represent different interfacial affinities. The DNS show that the logarithmic region is largely preserved, aside from an approximately constant upward shift, while the near-wall turbulence is modified through changes in the streamwise Reynolds stress. In particular, the streamwise turbulence intensity in the viscous sublayer is strongest when the mean wall stress is close to the slip-activation threshold, and it weakens as the mean stress moves away from that threshold. Analysis further indicates that shear-dependent slip reduces near-wall dissipation and promotes elongated near-wall coherent structures. Finally, a mean flow model that incorporates shear-dependent slip shows good agreement with the DNS mean velocity profiles. Overall, this work provides a multiscale framework that links molecular interfacial physics to continuum-scale turbulence.

Particle size segregation is a common occurrence in sheared granular flows under gravity. Segregation of size-bidisperse grain mixtures at size ratios of three or less has been extensively studied, but comparatively little is known about segregation of grains with more widely varying sizes, despite their relevance to natural and industrial flows. At larger size ratios the segregation behaviour of bidisperse mixtures may change drastically, including reversal of the direction of segregation, which no existing continuum model accounts for. This paper investigates the segregation behaviour of bidisperse granular mixtures up to a size ratio of seven and formulates a new continuum model for size segregation that captures the observed suppression and reversal of segregation. Discrete element method (DEM) simulations of flows on an inclined plane show a reversal of behaviour as the volume fraction of small particles increases, from states where the large particles rise to the free surface to states where they sink. At intermediate small-particle volume fractions, segregation is significantly reduced or even entirely absent, leading to well-mixed flows. In addition, a striking layering effect is observed at large size ratios, where large particles organise into distinct layers one particle thick, separated by thin bands of small particles. This layering is demonstrated both in simulations and, for the first time, in laboratory experiments. The continuum segregation model introduces a new bidirectional segregation flux that accounts for the reversal in segregation. The model is in good quantitative agreement with DEM simulations across a range of small-particle volume fractions.

We systematically investigate the multiplicity of flow states in centrifugal convection in water at about $40\,^\circ$C with Prandtl number $Pr = 4.3$ in a vertically aligned annulus in which the inner radius, the gap between the cylinders and the height all coincide (6 cm). This leaves two independent control parameters: the thermal driving, quantified by the Rayleigh number ${\textit{Ra}}$, and the rotation strength, expressed by the Froude number ${\textit{Fr}}$. We explore the range $2\times 10^{5} \le {{\textit{Ra}}} \le 10^{7}$ for ${{\textit{Fr}}} = 10$ and $100$ with direct numerical simulations (DNS). The states are characterised by the number of convection rolls in the mid-height cross-section. We show that the final state sensitively depends on the initial condition, leading to pronounced multistability and substantial variations in heat and momentum transport, while the range of attainable states is strongly restricted. We derive a theoretical estimate of the admissible roll numbers based on the Poincaré–Friedrichs inequality and demonstrate quantitative agreement with the DNS. We further show that, for larger ${\textit{Ra}}$, the range of possible states shrinks systematically due to an elliptical instability, providing a predictive framework for the selection and disappearance of coherent roll states in centrifugal convection.

Controlling multiphase flow in disordered media is central to diverse practical contexts. Although nanoparticles have been widely utilised to modify surface wettability, factors governing their effects on dynamic displacement patterns remain unclear. Here, we identify the criterion for nanoparticle-induced wettability alteration during displacement by combining interfacial-scale wetting models, pore-scale microfluidic experiments and simulations. Motivated by striking contrasts in static wettability, we find that nanoparticle adsorption on solid surfaces affects displacement interfaces only when spreading of wetting films is pre-established, corresponding to corner-flow conditions. Displacement experiments under varying intrinsic wettability show that wetting-film development and non-aqueous droplet detachment are strengthened exclusively on moderately water-wet surfaces satisfying the corner-flow criterion. Investigations across designed porous structures with varying degrees of structural hierarchy validate the generality of the wettability criterion, while improvement in displacement efficiency diminishes with reduced hierarchy. The structural effect arises from variations in flow heterogeneity, with stronger heterogeneity simultaneously promoting film flow and ganglion mobilisation. The coupled impacts of wettability and structural conditions are summarised in an illustrative phase diagram delineating nanoparticle-tuned multiphase displacement. Our findings offer mechanistic insights into complex fluid flow in porous media and suggest optimised strategies for displacement control via nanoparticle suspensions.

A benchmark road vehicle geometry – the square-back Windsor body with wheels and at zero yaw angle – is simulated using high-fidelity wall-resolved large eddy simulation. Passive control for drag reduction, in the form of optimisation of its rear roof extension, is performed. The rear roof extension is parameterised by its taper penetration distance, angle of incidence and length. This optimisation process uses Gaussian process-based surrogate modelling combined with Bayesian optimisation (Kriging), guided by an expected improvement criterion. The optimisation converged in six iterations (60 simulations), achieving a $6.5\,\%$ drag reduction. Six distinct drag-reduction mechanisms were identified: diffuser-induced pressure recovery, base-size reduction, vertical wake balance modification, separation effects, recirculation region core relocation and spanwise re-symmetrisation. Rather than isolating individual mechanisms, the study reveals how they interact when multiple geometric parameters are varied concurrently, providing a system-level picture that yields practical design rules. The optimal configuration was found at a roof extension angle of incidence corresponding to the onset of separation, with taper penetration distance and extension length at their maximum values within the analysed domain. These findings establish a robust framework for aerodynamic optimisation and reinforce the effectiveness of Bayesian optimisation in Computational Fluid Dynamics-based design. In this way, the work bridges fundamental wake studies with applied design practice, showing how coupled wake–geometry interactions can be harnessed for improved aerodynamic performance.

The propulsion speed of spheroidal squirmers was obtained by Keller & Wu (J. Fluid Mech., 1977, vol. 80, p. A31). It has become the benchmark to investigate the effect of shape on the propulsion of ciliated microorganisms. However, their study focused on translational motion whereas many biologically relevant organisms also experience rotational (or swirling) motion. We derive an analytical expression for the angular velocity of a swirling spheroidal squirmer. Our analysis reveals that spheroidal squirmers rotate faster than their spherical counterparts in Newtonian fluids. We also determine the contribution of the second azimuthal mode to the power dissipation generated by a spheroidal squirmer, and uncover a behaviour uniquely distinct from the power dissipation of a strictly translating swimmer.

Upon radial liquid sheet expansion, a bounding rim forms, with a thickness and stability governed, in part, by the liquid influx from the unsteady connected sheet. We examine how the thickness and fragmentation of such a radially expanding rim change upon its severance from its sheet, absent of liquid influx. To do so, we design an experiment enabling the study of rims pre- and post-severance by vaporising the thin neck connecting the rim. No vaporisation occurs of the bulk rim itself. We confirm that the severed rim follows a ballistic motion, with a radial velocity inherited from the sheet at severance time. We identify that the severed rim undergoes fragmentation in two types of junctions: the base of inherited, pre-severance, ligaments and the junction between nascent rim corrugations, with no significant distinction between the two associated time scales. The number of ligaments and fragments formed is captured well by the theoretical prediction of rim corrugation and ligament wavenumbers established for unsteady expanding sheets upon droplet impact on surfaces of comparable size to the droplet. Our findings are robust to changes in impacting laser energy and initial droplet size. Finally, we report and analyse the re-formation of the rim on the expanding sheet and propose a prediction for its characteristic corrugation time scale. Our findings highlight the fundamental mechanisms governing interfacial destabilisation of connected fluid-fed expanding rims that become severed, thereby clarifying destabilisation of freely radially expanding toroidal fluid structures absent of fluid influx.

This work studies the aerodynamics of two tandem foils flapping near a boundary layer (BL). The interaction between the tandem foils and the BL is modulated by the foil-to-wall distance rescaled by the foil chord length ($H_0/c$) and the Reynolds number based on free stream velocity (${\textit{Re}}=U_{\infty }c/\nu$). Taking the single foil under the same configuration as the reference, difference reductions are observed in forces between either of the tandem foils and the single foil, due to the weakened coupling between tandem foils in the presence of the BL. For a similar reason, it is revealed that, as ${\textit{Re}}$ increases, the force evolutions of the hind foil increasingly resemble those of the fore foil, being a second difference reduction. When examining the system’s evolution, we find that, in some cases, the evolution period of the force and the wake flow doubles that of the flapping cycle. From the Lagrangian coherent structures, it is indicated that this period doubling occurs because, in these cases, only one of two trailing edge vortices, shed in two successive cycles, is convected downstream, while the other is trapped and eventually dissipated in the BL. This interpretation has also been well confirmed by the frequency response from the modal analysis. In the cases with period doubling, the effect of the BL is relatively weak, corresponding to a coupling-dominated mode of interaction. Additionally, BL-dominated mode (low ${\textit{Re}}$ and/or low $H_0/c$) and foil-dominated mode (high ${\textit{Re}}$ and/or high $H_0/c$) are also identified, where the period doubling is not present anymore, respectively because of the strong BL effect and its absence. Finally, a bifurcation analysis is conducted to explore the dynamical nature of the system’s evolution. As $H_0/c$ increases, the system first undergoes a flip bifurcation, leading to the period doubling due to the decaying BL effect; and then an inverse period doubling bifurcation occurs, corresponding to a transition from coupling-dominated to foil-dominated interaction mode. If taking ${\textit{Re}}$ as the bifurcation parameter, a flip bifurcation is also first observed, sharing the same physical picture as the flip bifurcation identified when increasing $H_0/c$. Further increasing ${\textit{Re}}$, the system will undergo a Neimark–Sacker bifurcation due to the nonlinear nature of the convective flow, and the evolution of the system transitions from period doubling to quasi-periodic state.