Heat or mass transport due to forced convection is characterised by a relation of the form ${\textit{Nu}} = {\mathcal F}({\textit{Pe}})$. The Nusselt number, ${\textit{Nu}}$, is the non-dimensional heat or mass (scalar) transport rate and ${\textit{Pe}} = Ua/D$, the Péclet number, is a dimensionless parameter measuring the relative importance of convection and diffusion. Here, $a$ is the characteristic size of the particle or drop, $D$ the scalar diffusivity and $U$ an appropriate velocity scale; ${\textit{Nu}}$ is defined to be unity in the absence of a flow (${\textit{Pe}} = 0$). We attempt to understand the nature of the ${\textit{Nu}}{-}{\textit{Pe}}$ relationships that arise for scalar transport from suspended particles and drops. For the simple case of an ambient uniform flow convecting the scalar, a scenario that arises for a particle or drop translating relative to an otherwise quiescent ambient, ${\mathcal F}({\textit{Pe}})$ transitions from unity, to eventually increasing as a power of Pe, for large Pe. The large-Pe exponent is 1/3 for particles and 1/2 for drops, and is directly related to the thickness of the scalar boundary layer that develops on the particle (drop) surface at large Pe. Our main focus is on transport from neutrally buoyant particles and drops in linear shearing flows, in which case $U=\dot {\gamma }a$, $\dot {\gamma }$ being the ambient shear rate. Although Pe remains an important parameter, Nu now depends sensitively on the geometry of the linear flow. The latter determines the near-surface flow that, in turn, controls the nature of the boundary-layer-enhanced transport for large Pe. The topology of the near-surface streamlines or pathlines can vary widely, depending on ambient flow-type, leading to a variety of transport scenarios. Understanding the Nu–Pe relationships across this wide range is crucial to understanding transport in more complicated situations, including particles (drops) in turbulence.

The two-way interaction between the unsteady flame heat release rate (HRR) and acoustic waves can lead to combustion instability within combustors. Previous studies have typically characterised premixed flame responses to pure harmonic forcing, assuming dynamically linear or weakly nonlinear behaviour, to quantify flame–acoustic interactions. By combining third-order asymptotic analysis with numerical simulations of the $G$-equation, this study investigates the nonlinear response of laminar premixed V-flames subjected to dual-frequency velocity perturbations ($St_1$ and $St_2$, dimensionless frequencies). The positive correlation between disturbance propagation speed $u_c$ and frequency $St$ is captured by integrating a velocity-potential model with calibration against existing experimental data. The mechanism by which the disturbance at one forcing frequency, say $St_2$, affects the flame dynamic response at the other forcing frequency, $St_1$, is studied in detail. The perturbation at $St_2$ couples with that at $St_1$ to induce third-order nonlinear terms, giving rise to a non-monotonic suppression mechanism that smooths out the flame’s spatial wrinkling owing to the positive correlation between $u_c$ and $St$. As a result, excitation at $St_2$ modifies the HRR response at $St_1$, delineating an effective region bounded on the left by the frequency threshold of the linear response and on the right by the aforementioned non-monotonicity. Within this region, excitation at $St_2$ can markedly attenuate the HRR gain at $St_1$ compared with the case where the flame is driven solely by the perturbation at $St_1$. For instance, once both perturbation amplitudes exceed a certain threshold, excitation at $St_2$ can attenuate the flame response at $St_1$ by more than 40 % compared with the case without excitation at $St_2$. These findings contribute to the development of a quantitative framework for understanding how targeted frequency perturbations modulate the flame dynamics via nonlinear interactions, which may inform open-loop approaches for mitigating thermoacoustic instabilities in combustion chambers.

This work uncovers a counterintuitive effect of structural damping on vortex-induced vibrations (VIV). The influence of structural damping is examined numerically in the canonical problem usually considered to study these vibrations driven by flow-body synchronisation, i.e. a circular cylinder free to oscillate within a uniform cross-current, for Reynolds numbers up to $160$, based on the body diameter and inflow velocity. For rectilinear VIV without structural restoring force, the peak-amplitude responses, which develop for low structure to displaced fluid mass ratios, are always attenuated by damping, as previously reported. Yet, the lower-amplitude responses occurring for higher mass ratios exhibit a contrasting trend: they are amplified by damping. The amplification can be substantial and leads to vibrations that become significant compared with the peak-amplitude responses. It is observed over the entire Reynolds number range of VIV, and is even accompanied by an extension of this range in the subcritical region, relative to the threshold of $47$ that marks the onset of flow unsteadiness for a fixed body. The enhancement of VIV by structural damping is interpreted in light of the distribution of fluid–structure energy transfer in the amplitude–frequency domain. Such an enhancement is a counterintuitive but general phenomenon, which is shown to persist along curvilinear trajectories and when a structural restoring force is added to the system.

Chiral particles are experimentally investigated while settling in water with various turbulence intensity levels. The locations and orientations of the particles are tracked over time, allowing the close investigation of the particles’ settling dynamics. The generated turbulent flow is measured using laser Doppler anemometry, and the turbulence strength varies between experiments in the range $0 \leqslant \textit{Re}_\lambda \leqslant 250$. Starting with quiescent particle settling, the chiral particle’s orientation dynamics is studied, revealing a preferred alignment and a strong translation–rotation coupling. The particle chirality determines the preferred rotation direction, though the alignment and translation–rotation coupling gradually weaken with increasing turbulence. We identify multiple settling modes for the chiral particles, which are characterised by the evolution of the rotation angles. Finally, a theoretical model assuming a simplified chiral particle in Stokes flow clarifies the emergence of each settling mode.

The linearised Navier–Stokes (LNS) equations are employed in channel flow to study linear amplification mechanisms from an input–output point of view. We consider two models: the full LNS system and a simplified model. In the simplified model, we retain only the forcing pathways that pertain to the shear-driven lift-up mechanism. This approach enables individual analysis of the Orr–Sommerfeld and Squire operators as subsystems, revealing the relationship between linear amplification and the linear mechanisms from which it arises. We examine wavenumber regions corresponding to streamwise streaks, oblique waves and Tollmien–Schlichting (TS) waves, linking the underlying mechanisms back to the LNS equations. Analysis is performed for laminar Poiseuille flow, laminar Couette flow and turbulent Poiseuille flow using an eddy-viscosity model. Results indicate that the Orr–Sommerfeld system amplifies regions for streamwise streaks, oblique waves and TS waves, whereas the Squire system only amplifies streamwise streaks and oblique waves. Leading modal structures between the full and simplified models are also compared.

Droplet impingement is one of the most common phenomena in nature. However, the impact dynamics of droplets on structured heterogeneous wettability surfaces remain little explored. In this work, an investigation is conducted into the droplet impact on heterogeneous wettability surfaces composed of superhydrophobic micropillars on a hydrophilic substrate, by using an improved phase-field lattice Boltzmann model. In particular, the effects of surface geometry and impact conditions on droplet bouncing and wetting behaviours are scrutinised. Four distinct impact outcomes are identified: complete bouncing, pancake bouncing, partial wetting and complete wetting. Based on the competition among capillary, inertial and viscous forces, an analytical model is proposed to predict the maximum droplet penetration depth within the pillar gaps. A transition diagram is constructed to distinguish these different impact outcomes, with regime boundaries derived from the proposed analytical model. Finally, from the perspective of energy analysis, both the evolution of the energy budget and the surface energy distribution during the droplet impact process are revealed. These findings provide guidance for the design of heterogeneous wettability surfaces, enabling predictable control over droplet bouncing and wetting behaviours.

The Lagrangian-averaged Navier–Stokes-$\alpha$ (LANS-$\alpha$) model, a turbulence closure scheme based on energy-conserving modifications to nonlinear advection, can produce more energetic simulations than standard models, leading to improved fidelity (e.g. in ocean models). However, comprehensive understanding of the mechanism driving this energetic enhancement has proven elusive. To address this, we derive the fast quasi-geostrophic limit of the three-dimensional, stably stratified LANS-$\alpha$ equations. This provides both the slow, balanced flow and the leading-order fast wave dynamics. Analysis of these wave dynamics suggests that an explanation for the energetic enhancement lies in the dual role of the smoothing parameter itself: increasing $\alpha$ regularises the dynamics and simultaneously generates a robust landscape of wave–wave resonant interactions. Direct numerical simulations show that $\alpha$ plays an analogous role to the Burger number (${\textit{Bu}}$) in governing the partition of energy between slow and fast modes – and, consequently, the time scale of geostrophic adjustment – but with key differences. Increasing $\alpha$, regardless of the relative strengths of rotation and stratification, extends the persistence of wave energy by delaying the dominance of the slow modes. We find that the creation of an energy pathway involving only fast waves is a universal outcome of the regularisation across all values of ${\textit{Bu}}$, accompanied by a restructuring of slow–fast–fast interactions. These insights unify the LANS-$\alpha$ model’s characteristic energetic enhancement with, in some cases, its known numerical stiffness, identifying potential pathways to mitigate stability issues hindering the broader application of LANS-$\alpha$-type models.

This study investigates the unsteady oscillation cycle of sheet and tip vortex cavitation over an elliptical NACA $66_2$-415 hydrofoil using high-speed imaging and time-resolved tomographic particle image velocimetry. Synchronised measurements of radiated noise are conducted. The oscillation cycle consists of three phases, involving growth and collapse of the sheet and tip vortex cavitation, followed by intermittent rebounding of the tip vortex cavity. The collapse of the sheet cavity is triggered by a side-entrant jet, leading to the formation of the cloud and secondary vortex cavitation. The interaction between the secondary and tip vortex cavities further promotes the collapse of the latter. The three-dimensional instantaneous flow organisation indicates that the evolution of cavitation affects the centre displacement, deformation and breakdown of the tip vortex. Spanwise vortices emerge and interact with the tip vortex after the growth phase, causing violent fluctuations of the tip vortex during the collapse phase. The intense interaction between these vortices enhances the perturbation growth and promotes tip vortex breakdown. Proper orthogonal decomposition analysis reveals that the dominant unstable modes near the hydrofoil tip correspond to the displacement and deformation types. In addition to the suction-side shear layer, the vortex interaction region also exhibits intense production of turbulent kinetic energy. The temporal variation of sound pressure over an oscillation cycle indicates a strong correlation with the cavity morphology.

We are concerned with the nonlinear modelling of three-dimensional internal gravity waves in the lower atmosphere. A simplified configuration of density stratification is adopted, assuming that the atmosphere consists of two layers of uniform density with a sharp interface between the two bulk fluids. A time-dependent topography is considered to model a non-uniform, time-varying background current over variable terrain. Based on the Ablowitz–Fokas–Musslimani formulation for irrotational flows, both fully and weakly nonlinear long-wave isotropic models are derived in the Benjamin–Ono regime, where the upper layer is set to be semi-infinite. Two atmospheric gravity wave phenomena, motivated by satellite observations, are simulated using two modified numerical schemes to showcase the newly developed nonlinear models: the internal wave wake in the downwind zone behind a local topographic high and concentric ring waves, which appear as arched cloud formations along wave crests.

We present a robust optimisation framework for computing invariant solutions of wall-bounded flows by recasting the Navier–Stokes equations as a variational problem as established in Ashtari & Schneider (J. Fluid Mech., vol. 977, 2023, A7). The approach minimises the residual of the governing equations over a finite-time horizon, seeking periodic or equilibrium solutions. A novel contribution is made by including a Galerkin projection onto a basis of divergence-free modes that satisfy the no-slip boundary conditions. This projection not only makes the variational framework applicable to wall-bounded flows but it also yields a low-order representation of the dynamics. The basis is derived from resolvent analysis, which provides an orthonormal set. We demonstrate the method on a streamwise invariant formulation of rotating plane Couette flow, obtaining exact equilibrium and periodic solutions consistent with direct numerical simulations. The conditioning of the optimisation problem is analysed in detail, showing that convergence rates depend on the stability properties of the targeted solutions. Finally, we highlight a direct link between the conditioning of the optimisation and the structure of the resolvent operator, suggesting a unifying perspective on both the efficiency of the optimisation and the dynamical significance of resolvent modes.

Direct numerical simulations are performed on compressible turbulent boundary layers with micro-blowing controls applied to the walls at a free stream Mach number of 2.0 to investigate the influences of wall-blowing mass flux and spatial arrangements on drag reduction. Using law-of-the-wall for uniform blowing control, an estimation of skin friction is proposed based on Reynolds number and wall-blowing mass flux. At a given Reynolds number, the drag reduction rate increases almost logarithmically with wall-blowing mass flux within the control region. Downstream of the interaction zone, the drag reduction rate increases linearly. The disparities of the drag reduction rate in the integral sense among cases with different spatial arrangements are attributed to the asymmetric pressure gradient associated with flow compression, and expansion at the commencement and termination of the micro-blowing region.

We investigate viscoelastic flow past a square cylinder using the Phan-Thien–Tanner model to disentangle the competing effects of elasticity and shear-thinning. Simulations cover Weissenberg numbers ranging from 0.1 to 10 000, at a fixed Reynolds number of 10 and a solvent viscosity ratio of 0.6. The results are compared with the Newtonian, Oldroyd-B and Carreau–Yasuda models to isolate the influence of each rheological mechanism on drag, vortex shedding and wake structure. For Weissenberg numbers less than 50, elastic stresses dominate; drag increases by up to 30 %, vortex shedding is delayed as the critical Reynolds number increases by approximately 18 %, and the wake contracts sharply, with recirculation lengths reduced by up to 85 %. In the intermediate regime, where Weissenberg numbers range from 50 to 500, elasticity generates distinctive features, including asymmetric upstream vortices, triangular vortex cores and persistent upstream vortices, with their lifetimes increasing with the retardation ratio. For Weissenberg numbers greater than 500, shear-thinning becomes dominant, restoring behaviour similar to that of Newtonian fluids. Vortex lengths recover, drag decreases steadily, the critical Reynolds number drops and the shedding frequency increases by 15%–40 %, depending on fluid extensibility. These results reveal that the interaction between elasticity and shear-thinning controls wake dynamics through a complex balance.

As insects flap their wings, they generate complex wake structures critical to their aerodynamic force production. Specific flow structures such as the leading-edge vortex have been studied for decades; however, a complete understanding of the transient dynamics and energy exchange mechanisms in insect wakes remains elusive. To help bridge this gap, we employ data-driven reduced-order modelling techniques to identify a simple and interpretable model for a hovering hawkmoth’s wake. We begin by using an in-house immersed-boundary-method computational fluid dynamics solver to simulate hovering hawkmoth flight. We then perform dynamic mode decomposition to distil the resulting flow field into a set of time-varying modes. Finally, we employ sparse regression to identify a model capturing the driving modes’ temporal evolution, ranging from quiescent flow to periodic steady state. Notably, the model takes the form of a Stuart–Landau oscillator with higher-order nonlinear terms. The presence of a limit-cycle dynamics suggests a balance between energy input from wing motion and energy lost due to advective energy transfer and viscous dissipation. Using an impulse-based wake survey method, we show that this model provides an accurate estimation (mean absolute error within 3.5 % of body weight) of the hawkmoth’s long-term lift production. These findings highlight the significance of stability and energy transfer in flapping-flight aerodynamics, offering a framework for future studies of biological flight systems. Furthermore, by linking the wake dynamics to simple dynamic equations, this work provides inspiration for the design and control of bio-inspired micro-aerial vehicles.

Drop deformation and motion driven by shear flows are widespread phenomena in nature and underpin a variety of technological applications. We investigate the deformation, motion and contact-line dynamics of two-dimensional drops in steady shear flows within the framework of lubrication theory. For pinned drops with $180^\circ$ hysteresis, we identify a critical shear rate, beyond which the upstream side becomes unstable and a thinning film develops. At late stage, the thinning film connects to the bulk drop through a self-similar capillary transition structure. For moving drops with $0^\circ$ hysteresis, the dynamical behaviours can be classified into three regions: in the low-shear region, the steady-state drop velocity increases linearly with the shear number $S$; in the intermediate-shear region, the drop velocity exhibits a non-monotonic dependence on $S$; in the high-shear region, the steady-state drop profile can be clearly divided into the entrained film, dimple and capillary ridge. Moreover, during the drop evolution under high shear, a Landau–Levich–Derjaguin-like (LLD-like) film emerges and exhibits a scaling law that differs from the classical LLD law. These results provide a unified theoretical and numerical framework for understanding shear-driven drop dynamics and may offer insights into analogous three-dimensional systems.

We investigate the effect of the transverse aspect ratio ($B$) of a thermogravitational column (TGC) on the stability of a binary fluid mixture with a negative separation ratio ($\psi$), which generates an adverse vertical density gradient. In extended systems, this configuration is unstable and limits separation. Here we show that confinement fundamentally alters this behaviour and can fully suppress the instability. Combining linear stability analysis of the three-dimensional basic state, three-dimensional simulations and experiments, we identify $B$ as the key control parameter. Linear stability analysis yields a correlation for the critical aspect ratio $B_{\textit{c}}(\psi )$ separating unstable and stable regimes. For $B \lt B_{\textit{c}}$, the system remains in a quiescent state despite the presence of the adverse density stratification. Energy budget analysis shows that confinement enhances transverse diffusive transport, preventing the growth of long-wave instabilities that dominate in extended systems. Direct numerical simulations confirm the predicted transition and reveal the nonlinear evolution towards convection when $B \gt B_{\textit{c}}$. Experiments performed with different mixtures, Tol$|$Ch 0.50$|$0.50, Tol$|$EtOH 0.80$|$0.20 and Tol$|$MeOH 0.8420$|$0.1520, and geometries using two independent $\mu$TGCs ($B$ = 5.88 and $B$ = 1.69) validate the theoretical predictions. These results demonstrate that transverse confinement provides a robust and tunable mechanism for controlling thermogravitational stability.

An experimental investigation is conducted to examine aeroacoustic instabilities in high-speed rectangular dual-impinging jets (DIJs), with a focus on the modal dynamics responsible for tonal noise generation. Comparisons are made with a circular baseline over expanded Mach numbers M = 1.0–1.2, impinging distances h/D = 2–3 and a fixed centre-to-centre spacing of S/D = 3.5. Time-resolved wall-pressure fields on the impingement plate and far-field sound are measured synchronously using fast-response pressure-sensitive paint and microphones. Dominant impingement tones and their associated surface-pressure patterns are identified and linked using cyclostationary spectral proper orthogonal decomposition and coherent output power analysis. Both circular and rectangular DIJs exhibit an annularly symmetric impingement mode whose tonal frequency is broadly consistent with classical single-loop jet–plate feedback scaling. In the rectangular configuration, this mode develops an elliptical footprint and a reduced dual-jet interference region, leading to attenuation of the corresponding tone relative to the circular case. In addition, rectangular DIJs support a flapping antisymmetric plate-pressure mode characterised by alternating pressure-wave orientations and a four-stage evolution over the oscillation cycle. This mode is associated with a prominent tone at Strouhal number St = 0.42, which departs from the integer harmonics of the baseline feedback loop. Finally, a co-resonance framework is employed to interpret why the geometry-enabled tone is strongly amplified under the present dual-jet conditions. Overall, these results demonstrate that transitioning from circular to rectangular nozzles redistributes modal dominance in high-speed DIJs and reorganises the balance between attenuated harmonic peaks and an additional geometry-enabled tone.

Controversy exists regarding whether grain morphology reduces or enhances the drag of a single grain in creeping flows. Further complication occurs when orientation dependence of aspherical grains comes into play. To bridge this gap, this study investigates numerically the drag on fractally rough grains depicted by spherical harmonics. Rough shapes could induce drag reduction, indicated by a lower mean value of drag coefficients $C_{\!D}$ at various rotation angles, compared with that of the corresponding smooth sphere. Moreover, the derived power law between $C_{\!D}$ and the projected area $A_{\!p}$ perpendicular to the flow direction, expressed as $C_{\!D}\propto {A_{\!p}}^{-0.8}$ for spheroidal and triaxial-ellipsoidal grains, remains valid for irregular shapes. Such a rotational dependence helps to explain the paradox where drag enhancement is consistently encountered in settling grain experiments prevalent in geophysics. The macroscopic observations are elucidated by microanalysis on the fluid–grain contact pressure differences relative to the volume-equivalent sphere, revealing that the net drag reduction is mainly rooted in the frictional drag. By gaining a deeper understanding of the drag force on rough grains, this research provides valuable insights into particle–fluid interactions in creeping flows, and holds promising implications for unresolved simulations of fluid–particle systems.

This study develops wavenumber–frequency spectrum models for wall-pressure fluctuations in turbulent boundary layers on flat plates and cylinders in compressible flow. Through non-dimensionalisation and solution of the momentum and continuity equations, a unified physical framework integrating near-field pressure and far-field acoustic regions is established, extending Lighthill’s acoustic analogy. Starting from the fluctuating pressure governing equation, Mach number effects in the acoustic region are explicitly introduced for the first time, and unified analytical expressions across the full wavenumber range are derived for both geometries. The proposed models achieve high-precision prediction across the entire wavenumber domain. Validation is performed via cylinder wind tunnel experiments at Mach $0.12$–$0.18$ and flat-plate direct numerical simulation (DNS) at Mach $0.1$–$0.5$. Compared with classical models such as Chase II, Smol’yakov and Corcos, the present model shows better agreement with experimental and DNS data, particularly in low-wavenumber and acoustic regions, improving prediction accuracy by more than $10$ dB. Key findings: (i) acoustic amplitude highly correlates with Mach number, while the convective ridge does not; (ii) the acoustic of flat-plate boundary is defined by $k_{1}^{2} + k_{3}^{2} - (k_{0} - Mak_{1})^{2} = 0$, where $k$ is the wavenumber and $Ma$ is the Mach number; (iii) the cylinder model degenerates to the flat-plate form as the curvature radius approaches infinity, with curvature effects confined mainly to the acoustic region and large circumferential wavenumbers. This work provides a physically self-consistent and practical engineering spectral model with significantly enhanced predictive capability under compressible-flow conditions.

This study employs synthetic jet actuation (SJA) to control large-scale flow separation on the suction side of a NACA0015 aerofoil at a Reynolds number of 2.1 $\times$ $10^5$ and an angle of $18^\circ$. The underlying control mechanism is investigated using large-eddy simulations to resolve the dynamics of jet-induced coherent structures associated with the low-frequency actuation. During the periodic blowing and suction cycle, two distinct types of spanwise coherent vortices are identified: blowing-induced vortices (BIVs) and suction-induced vortices (SIVs), which differ significantly in spatial distribution and energy content. As these vortices are convected downstream at speeds comparable to the free-stream velocity, BIVs exhibit a significantly slower rate of energy decay, whereas SIVs dissipate rapidly, particularly near the trailing edge. Triple decomposition analysis shows that energy addition is primarily associated with the coherent velocity components. Notably, BIVs exhibit a stronger entrainment capacity, enhancing momentum exchange between the separated shear layer and outer flow via coherent Reynolds shear stresses. This intensified exchange facilitates the outward transport of low-momentum fluid, effectively enhancing aerodynamic performance and delaying flow separation. Furthermore, spectral proper orthogonal decomposition reveals distinct energy peaks centred at the actuation frequency and its harmonics. Among the two vortex types, BIVs contribute most of the coherent spectral energy, highlighting their critical role in the overall effectiveness of the flow control. These findings elucidate the flow organisation and modulation mechanisms associated with low-frequency SJA under deep-stall conditions, and provide a physical interpretation of the observed reorganisation of the separated flow.