The clustering of inertial particles in turbulent flows is ubiquitous in many applications. This phenomenon is attributed to the influence of multiscale vortex structures in turbulent flows on particle motion. In this study, our primary goal is to further investigate the vortex effect on particle motion. We perform analytical and numerical simulations to examine the motion of particles in a counter-rotating vortex pair (CVP) with circulation ratio $\gamma \in (-1,0)$. The small, dilute, heavy inertial particles with a low particle Reynolds number are considered. In particular, the particle Stokes number and density factor satisfy $St\in (0,0.3)$ and $ R\in (0,1)$, respectively. We validate the existence of a particle-attracting ring within the CVP, which provides a simple mechanism for particle trapping. Meanwhile, there exists a critical Stokes number $St_{{cr}}$ limiting the occurrence of particle trapping. We provide a formula to predict the value of $St_{{cr}}$, which depends on both $\gamma$ and $R$. Only when $St\lt St_{{cr}}$ can the attracting ring trap the particle initially located within its basin of attraction and eventually lead to the formation of a particle clustering ring. Particles with a larger $R$ are more likely to be trapped in the CVP. While $St\gt St_{{cr}}$, the dynamics of the particles exhibits finite-time ‘leakage’. The attracting ring in the phase space coincides with the saddle point from which particles escape. Although all particles eventually escape, some may remain trapped in the vortex core region for a duration (represented by residence time). The distribution of residence time exhibits a localised exponential-like feature, indicating transient chaos.

Inspired by small intestine motility, we investigate the flow induced by a propagating pendular wave along the walls of a channel lined with rigid, villi-like microstructures. The villi undergo harmonic axial oscillations with a phase lag relative to their neighbours, generating travelling patterns of intervillous contraction. Using two-dimensional lattice Boltzmann simulations, we resolve the flow within the villi zone and the lumen, sampling small to moderate Womersley numbers. We uncover a mixing boundary layer (MBL) just above the villi, composed of semi-vortical structures that travel with the imposed wave. In the lumen, an axial steady flow emerges, surprisingly oriented opposite to the wave propagation direction, contrary to canonical peristaltic flows. We attribute this flow reversal to the non-reciprocal trajectories of fluid trapped between adjacent villi and derive a geometric scaling law that captures its magnitude in the Stokes regime. The MBL thickness is found to depend solely on the wave kinematics given by intervillous phase lag in the low-inertia limit. Above a critical threshold, oscillatory inertia induces dynamic confinement, limiting the radial extent of the MBL and leading to non-monotonic behaviour of the axial steady flux. We further develop an effective boundary condition at the villus tips, incorporating both steady and oscillatory components across relevant spatial scales. This framework enables coarse-grained simulations of intestinal flows without resolving individual villi. Our results shed light on the interplay among active microstructure, pendular wave and finite inertia in biological flows, and suggests new avenues for flow control in biomimetic and microfluidic systems.

The electrokinetic and unstable behaviour near strongly polarised surfaces cannot be well captured by the canonical asymptotic theory for induced-charge electro-osmosis, and the intrinsic mechanism remains unclear. Using direct numerical simulations and scaling analysis, this paper reveals that, near the strongly polarised surfaces, the strong electric double layer charging induces a strong local electric field, which drives the cations in the electrical double layer to extend to a finite region and form an extended space-charge (ESC) layer. The ESC triggers flow instability near strongly polarised surfaces, causing a transition of the velocity scaling exponent in the electric field dependence from a 2 to a 4/3 power law. The findings and mechanisms pave the way for designs of energy and biomedical systems.

Single-cell tornado-like vortices (TLVs) exhibit periodic wandering fluctuations around the time-averaged vortex core, a phenomenon known as vortex wandering, which constitutes the most prominent periodic behaviour in such flows. The coupling between vortex motion and wandering creates complex swirl dynamics, posing significant analytical challenges. However, the limited availability of experimental studies on vortex wandering decomposition hampers a deeper understanding of this phenomenon. To address this gap, a tornado simulator was designed to generate a controllable single-cell TLV, and high-frequency velocity data were obtained using particle image velocimetry. A sparsity-promoting dynamic mode decomposition (sp-DMD) method was developed to decouple coherent structures and analyse dynamic characteristics. Results show that as the swirl ratio increases, the vortex structure becomes more diffuse, with significant reductions in intensity. Vortex wandering is present across all swirl conditions, with its periodicity strongly modulated by the swirl ratio. Importantly, sp-DMD identified two primary modes, the time-averaged mode (first mode), representing the dominant rotational vortex motion, and the vortex-wandering-dominated modes (second and third conjugate modes), which correspond to persistent periodic velocity fluctuations and contribute the most significant pulsations. These modes exhibit a pair of oppositely rotating vortices symmetrically revolving around the central flow axis. Visualisations of the Q criterion reveal a symmetric dipole pattern. This suggests that rotational and shear effects are likely responsible for the periodic movement of the vortex core. Furthermore, as the swirl ratio increases, the energy of the vortex-wandering-dominated modes diminishes, and motion transitions from high-energy, organised dynamics to low-energy, disordered behaviour.

This paper presents an experimental and analytical investigation of the turbulent transport and flame geometric characteristics of free turbulent buoyant diffusion flames under different fuel mass fluxes and burner boundary conditions (i.e. with/without a flush floor). The stereo particle image velocimetry technique was utilised to measure the three-dimensional instantaneous velocity fields of the free methane buoyant flames with a burner diameter (d) of 0.30 m and dimensionless heat release rates ($\dot{Q}^{*}$) of 0.50–0.90. The results showed that, compared with the configuration without a floor, the time-averaged axial velocity fluctuations squared and the time-averaged radial velocity fluctuations squared decreased, and the peak values of the time-averaged radial velocity, the time-averaged radial velocity fluctuations squared and the time-averaged axial and radial fluctuation product shifted towards the burner centreline in the configuration with a flush floor. Based on the dimensional analysis and the gradient transport assumption, the mean turbulent viscosity within the mean flame height ($\nu _{t}^{=}$) was scaled. Compared with the configuration without a floor of under equal $\dot{Q}^{*}$, the turbulent viscosity decreased in the configuration with a flush floor, resulting in an increase in mean flame height and a reduction in mean flame width. Based on the concepts of turbulent mixing and equal axial convection and radial diffusion times, semi-physical models were derived for the mean flame height and the mean flame width, respectively. The two correlations agreed well with the experimental data of this work for the two burner configurations with and without a flush floor.

Stress–velocity cross-spectra provide critical insights into the wall turbulence dynamics, where second-order cross-spectra have been used to characterise the amplitude modulation of large-scale motions on smaller scales. Here, we investigate the higher-order stress–velocity cross-spectra. Through theoretical analysis, we derive an exact relationship demonstrating that the difference in convection velocity between streamwise Reynolds normal stress fluctuations ($r$) and streamwise velocity fluctuations ($u$) – termed the $r{-}u$ convection velocity difference – is governed jointly by the second- and fourth-order cross-spectra. A new ‘coherence similarity’ (CS) model is proposed, which reveals an approximate similarity between higher-order and second-order cross-spectra. As a result, the $r{-}u$ convection velocity difference can be explained in terms of second-order cross-spectral properties. Numerical validation confirms that the CS model predicts higher-order cross-spectra and the convection velocity difference accurately. Furthermore, the contours of stress–velocity cross-spectra undergo a structural transition from single-lobe to triple-lobe patterns with increasing wall distance, suggesting the presence of complex space–time coupling between $r$ and $u$.

This study uses a coupled lattice Boltzmann and discrete element method to perform interface-resolved simulations of turbulent channel flow laden with finite-size cylindrical particles. The aim is to investigate interactions between wall-bounded turbulence and non-spherical particles with sharp edges. The particle-to-fluid density ratio is unity and gravity is neglected. Comparative analyses are conducted among long (length-to-diameter aspect ratio 2), unit (1) and short ($ 1/2 $) cylinders, along with spheres and literature data for spheroids. Results reveal both shared and distinct dynamic behaviours of cylinders and their effects on turbulence modulation. Notably, disk-like short cylinders can remain trapped near the wall due to their flat faces aligning closely with it – a behaviour unique to particles with sharp edges. Long and unit cylinders, as well as spheres, preferentially accumulate in high-speed streaks, while short cylinders cluster in low-speed streaks, demonstrating a strong aspect-ratio effect. Near the wall, long cylinders align their axis with the streamwise direction, while short cylinders orient perpendicular to the wall. Rotationally, long cylinders primarily spin, whereas short ones predominantly tumble. These trends arise from orientation preferences and differences in axial and spanwise moments of inertia. Cylindrical particles increase wall drag compared with the single-phase case, with short cylinders causing the greatest enhancement due to strong near-wall accumulation. Overall, the influence of aspect ratio on particle dynamics and turbulence modulation is more pronounced for cylindrical particles than for spheroidal ones.

In this work we propose a neural operator-based coloured-in-time forcing model to predict space–time characteristics of large-scale turbulent structures in channel flows. The resolvent-based method has emerged as a powerful tool to capture dominant dynamics and associated spatial structures of turbulent flows. However, the method faces the difficulty in modelling the coloured-in-time nonlinear forcing, which often leads to large predictive discrepancies in the frequency spectra of velocity fluctuations. Although the eddy viscosity has been introduced to enhance the resolvent-based method by partially accounting for the forcing colour, it is still not able to accurately capture the decay rate of the time-correlation function. Also, the uncertainty in the modelled eddy viscosity can significantly limit the predictive reliability of the method. In view of these difficulties, we propose using the neural operator based on the DeepONet architecture to model the stochastic forcing as a function of mean velocity and eddy viscosity. Specifically, the DeepONet-based model is constructed to map an arbitrary eddy-viscosity profile and corresponding mean velocity to stochastic forcing spectra based on the direct numerical simulation data at $Re_\tau =180$. Furthermore, the learned forcing model is integrated with the resolvent operator, which enables predicting the space–time flow statistics based on the eddy viscosity and mean velocity from the Reynolds-averaged Navier–Stokes (RANS) method. Our results show that the proposed forcing model can accurately predict the frequency spectra of velocity in channel flows at different characteristic scales. Moreover, the model remains robust across different RANS-provided eddy viscosities and generalises well to $Re_\tau =550$.

The path followed since Faraday’s first observations of acoustic streaming has led to a modern picture of this field as split into separate panels of a tryptic: standing acoustic waves in a channel with uniform background density, known as Rayleigh–Schlichting streaming, with stratified background density, known as baroclinic streaming, and acoustic waves progressing far from the walls under the shape of an attenuated beam, known as Eckart streaming. In their theoretical work, Mushthaq et al. (2025 J. Fluid Mech. 1017, A32) describe in a single continuous parameter space both Rayleigh–Schlichting and baroclinic streaming, thus making a decisive step forward in the frontier between two of these panels. Dealing with a stratification of thermal origin, they identify the level of heating above which baroclinic streaming becomes of the same order of magnitude or greater than Rayleigh–Schlichting streaming. They also depict the major part played by the channel size to wavelength ratio in this problem. This work will be of great help in designing the next generation of experiments concerning acoustic streaming and acoustic management of heat transfer. It is of interest for engineering fields like microfluidics, electronics cooling and biomedical applications. It can also serve as an inspiring basis for academic works in which waves are crossed with stratification.

Direct numerical simulations of two-phase, free-surface flow past a fully submerged, fixed circular cylinder are conducted for transitional Reynolds numbers $400 \leqslant {\textit{Re}} \leqslant 2000$, with Weber number ${\textit{We}} = 1000$, Froude number ${\textit{Fr}} = 1$ and a fixed gap ratio $G = 0.5$. This parameter combination corresponds to the gas entrainment regime characterised by the production of multiscale gas bubbles through interface breakup in the wake, which is of particular interest for its implications in enhancing gas transfer and mixing in environmental and engineering flows, such as air–water gas exchange processes in rivers and oceans, and the design and performance of naval and offshore structures. For ${\textit{Re}}= 400$, the jet forced through the $0.5D$ gap where $D$ is the diameter of the cylinder, efficiently convects opposite-signed vorticity downstream, suppressing the classical von Kármán instability and yielding a quasisteady recirculation bubble. The jet’s stabilising influence, however, breaks down once ${\textit{Re}} \approx 500$: periodic vortex shedding re-emerges and the wake becomes unsteady in spite of the continuing jet. The corresponding dimensionless shedding frequency Strouhal number $St$ grows with ${\textit{Re}}$ as $0.52-72.7{\textit{Re}}^{-1}$. The onset of unsteadiness first shortens the mean separation length but then drives it towards a saturation plateau for higher ${\textit{Re}}$ values. Surface rupture in the turbulent wake fragments entrained air into a multiscale bubble population whose number density follows $S_b(R_{\textit{eff}}) \propto R_{\textit{eff}}^{-6}$, consistent with gravity–capillary breakup in breaking waves, where $R_{\textit{eff}}$ represents the effective radii of the bubbles. Intermittency in entrainment corresponding to vortex shedding contrasts sharply with the finger-like structures observed under laminar conditions, underscoring the role of turbulent mixing. The coupled analysis of vorticity transport, shear-layer instability and bubble statistics elucidates how momentum exchange and air entrainment over a submerged body are governed under non-turbulent and turbulent conditions.

Statistical structure and the underlying energy budget of wall-shear-stress fluctuations are studied in both Poiseuille and Couette flows with emphasis on its streamwise component. Using a dimensional analysis and direct numerical simulation data, it is shown that the spectra of streamwise wall dissipation for $\lambda \lesssim 1000 \delta _\nu$ are asymptotically invariant with the Reynolds number (${\textit{Re}}$), whereas those for $\lambda \gtrsim \delta$ decay with ${\textit{Re}}$ (here, $\lambda$ is a nominal wall-parallel wavelength, and $\delta _\nu$ and $\delta$ are the viscous inner and outer length scales, respectively). The wall dissipation increases with ${\textit{Re}}$ due to the increasing contribution of the spectra at $1000 \delta _\nu \lesssim \lambda \lesssim \delta$. The subsequent analysis of the energy budget shows that the near-wall motions associated with these wall-dissipation spectra are driven mainly by turbulent transport and are ‘inactive’ in the sense that they contain very little Reynolds shear stress (or turbulence production). As such, turbulent-transport spectra near the wall are also found to share the same ${\textit{Re}}$-scaling behaviour with wall dissipation, and this is observed in the spectra of both the wall-normal and inter-scale turbulent transports. The turbulent transport underpinning the increase of wall dissipation with ${\textit{Re}}$ is characterised by energy fluxes towards the wall, together with inverse energy transfer from small to large length scales along the wall-parallel directions.

We highlight the complete transition from liquid-wall-film instability of an annular gas–liquid flow inside a nozzle to spray formation at the trailing edge, aiming to identify two distinct flow regimes of ripple waves and disturbance waves and to clarify their distinct fragmentation mechanisms. Experiments conducted under strictly controlled boundary conditions support our theoretical analysis, revealing that the onset of disturbance waves coincides with the liquid-film Weber number (${\textit{We}}$) of unity, marking a significant change in following fragmentation dynamics. For ${\textit{We}}\lt 0.5$, the liquid wall film forms three-dimensional ripple waves driven by the superposition of Kelvin–Helmholtz and Rayleigh–Taylor (RT) instabilities, with no disturbance waves present. At the trailing edge, the liquid film temporarily accumulates, extends into isolated ligaments along the axial direction via RT instability, and subsequently fragments into droplets through Plateau–Rayleigh instability, displaying a weak coupling between ripple wave dynamics and fragmentation. In contrast, for ${\textit{We}}\gt 0.5$, disturbance waves with long wavelengths and large amplitudes become prominent, superimposed on the base ripple waves. As these disturbance waves reach the trailing edge, they are spontaneously ejected as liquid sheets at the same frequency, forming transverse rims through RT instability and rapidly disintegrating into fine droplets. This regime demonstrates a direct coupling between disturbance-wave dynamics and fragmentation.

This work presents a comprehensive analysis of steady cone-jet electrospray (SCJ-ES) that captures the full range of its steady jet scales within the Taylor-cone electric field. We identify three fundamental regions, each governed by distinct scaling laws and dominant physical mechanisms: (i) the transition region, characterised by the balances that fix the emitted current; (ii) the charge convection-dominated region, where surface charge transport dominates total charge transport and the Taylor field drives jet acceleration; and (iii) the ballistic region, where the jet attains a fixed cylindrical scale before undergoing Rayleigh breakup into charged droplets. This refined theoretical framework harmonises existing models, particularly those using the Taylor–Melcher leaky dielectric model as an electrokinetic approximation for SCJ-ES. Notably, our newly proposed spatial scales achieve a remarkable collapse of published experimental SCJ-ES jet profiles. We also apply this framework to study the charge of resulting droplets using extensive literature data, observing significant differences between weak and strong electrolytes, consistent with recent findings.