The evolution of flow structure is fundamental to establishing an accurate framework for predicting turbulent energy dissipation, momentum transfer, and sediment and nutrient transport within and above flexible stem arrays. The dynamics of flexible stems plays a crucial role in shaping these physical features. In this paper, direct numerical simulations are performed to examine flow through a three-dimensional square array of flexible stems, with explicit consideration of flexibility ($K$) effects. The results provide a comprehensive characterisation of the coupled stem dynamics, flow distribution and vortex structures. Three distinct dynamical regimes are identified. For large $K$, the stems behave as nearly rigid, causing the flow to accelerate through the gaps while attenuating behind the stems. At intermediate $K$, a perfect lock-in occurs between the stem’s natural and oscillation frequencies, leading to large-amplitude vibrations and markedly altered flow characteristics. For small $K$, the oscillation amplitude decreases but deformation increases, producing irregular stem dynamics and complex flow features. The flow dynamics underlying these regimes is systematically elucidated. Furthermore, energy dissipation and sediment transport effects are quantified through hydrodynamic drag, bed shear stress, and root mean square bed shear friction distributions. The array with intermediate $K$ exhibits the highest energy dissipation efficiency, surpassing even the rigid configuration. The bed shear stress reaches a peak at the upstream edge of the array, whereas stem oscillation redistributes the flow momentum towards the upper canopy and the overlying flow, reducing velocity fluctuations near the bed. Finally, the mechanisms governing the structural dynamics and hydrodynamic forces are discussed in detail. This study offers new physical insights into flow–structure interactions within flexible stem arrays, and proposes an optimised strategy for improving energy dissipation in coastal protection applications.

Large eddy simulation (LES) on a cylindrical grid consisting of approximately 7 billion points is used to analyse the wake flow of a marine propeller equipped with propeller boss cap fins (PBCFs). Computations of the same propeller without this energy saving device (ESD) were also conducted, for comparison purposes. The results of the simulations demonstrate almost an order of magnitude mitigation of the minima of pressure and the maxima of vorticity at the core of the hub vortex. Meanwhile, a significant recovery of both streamwise and azimuthal momentum is achieved, with beneficial effects on the efficiency of propulsion. Additional, smaller vortices are shed by the PBCFs, having a negligible impact on the wake flow, if compared with the benefits allowed by the mitigation of the hub vortex. This is also the case of the turbulent stresses. The only exception is the region just downstream of the propeller plane, upstream of the instability of the hub vortex, where turbulence levels at the core of the hub vortex are still relatively low. However, within a few diameters downstream of the rotor, the instability of the stronger hub vortex shed by the propeller without PBCFs is the source of turbulent stresses more than an order of magnitude higher than those experienced in the wake of the propeller equipped with PBCFs. Meanwhile, the influence of the PBCFs on the outer region of the wake and especially on the tip vortices was found to be practically negligible.

This study examines the role of buoyancy-induced baroclinic vorticity production in the three-dimensional (3-D) wake transition behind an infinitely long heated square cylinder subjected to aiding and cross-flow buoyancy, using direct numerical simulation (DNS). A non-Oberbeck–Boussinesq (NOB) model is employed, requiring the solution of the full compressible Navier–Stokes equations to capture baroclinic effects under large-scale heating regimes. Simulations are carried out at a Reynolds number of $\textit{Re} = 300$ and a low Mach number ($M = 0.1$) to minimise compressibility effects, with air (Prandtl number $\textit{Pr} = 0.71$) as the working fluid. Previous studies have demonstrated that baroclinic torque significantly enhances the strength of 3-D wake structures, thereby promoting an earlier onset of three-dimensionality compared with the unheated case. However, these effects have been predominantly investigated in cross-buoyancy configurations, and the underlying mechanisms remain insufficiently understood. In the present study, the contributions of streamwise and spanwise baroclinic torque are systematically analysed to elucidate the mechanisms governing flow instability and organisation in thermally influenced wakes. The findings reveal a complex interplay between baroclinic torque and buoyancy, indicating that increasing heating levels weaken the 3-D wake under aiding-buoyancy conditions while strengthening it in cross-buoyancy configurations. Furthermore, the production of spanwise baroclinic torque, whether aligned with or opposed to local vortices, increases flow complexity and influences vortex shedding intensity and vortex dislocations. It also governs the contrasting wake behaviour, resulting in a symmetric wake under aiding buoyancy and an asymmetric wake under cross-buoyancy.

Symmetry-breaking in the near-wake of a wall-proximity sphere is a claussic problem. Yet a clear understanding of how the gap ratio ($G/D$) governs the evolution and suppression of spanwise flow asymmetry across different Reynolds numbers ($Re$) is still lacking. Here, direct numerical simulations combined with proper orthogonal decomposition and vorticity transport analysis are employed over $420 \leqslant Re \leqslant 600$ and $0.1 \leqslant G/D \leqslant 1.5$ to elucidate the wall-induced suppression of spanwise asymmetry. As $G/D$ decreases, four regimes are identified: asymmetric unsteady II, asymmetric unsteady I, symmetric unsteady and symmetric steady. Notably, the spanwise wake deflection reverses direction between the two asymmetric regimes, signalling a structural transition regulated by vortical competition. This corresponds to the transition from the alternating shedding of upper and lower hairpin vortices to the formation of longitudinal vortices (LV) that interact with wall-secondary vortices (WSV). Symmetry restoration is associated with merging and the emergence of the second harmonic of the dominant shedding frequency. Crucially, the wall effect homogenises the streamwise pressure gradient and velocity-gradients in the spanwise direction. This gradient homogenisation attenuates the asymmetric tilting of spanwise vorticity, thereby reducing the feedback that maintains the spanwise asymmetry of the shear layer. In asymmetric regimes, wake deflection is sustained by dominant spanwise-asymmetric vorticity tilting into streamwise and wall-normal components. In the symmetric regime, suppression of the spanwise deflection of the shear layer supports wake-symmetry recovery. These findings provide insights into symmetry-breaking in wall-proximity bluff-body wakes, and offer guidance for active flow control.

The effect of spanwise extension on the wake dynamics of flow past a wall-mounted prism is investigated using direct numerical simulations at Reynolds numbers $\textit{Re}_h=300$, $500$ and $1000$ and spanwise extents $b/h=1$, $3$ and $5$. A horseshoe vortex (HsV) system forms upstream of the prism in all cases, while in most flows the leading-edge shear layer undergoes Kelvin–Helmholtz (KH) instability, generating KH vortices that evolve into arch-shaped vortices (ArcV) and subsequently hairpin vortices (HV). As $\textit{Re}_h$ and $b/h$ increase, the wake exhibits increasingly complex vortex dynamics. At $\textit{Re}_h=300$, the HsV system remains stable. For $b/h=5$, the downstream wake exhibits a subharmonic associated with periodic alternation between two ArcV-to-HV evolution modes. At $\textit{Re}_h=500$, dual vortex-evolution modes persist for $b/h=3$ and $5$, accompanied by dual shedding frequencies. At $\textit{Re}_h=1000$, the HsV system becomes unstable for $b/h=3$ and $5$, generating streamwise-elongated braid vortices whose passage coincides with earlier destabilisation of the leading-edge shear layer. For $b/h=3$, the unstable HsV system exhibits two characteristic frequencies associated with coherent system-wide vortex dynamics. For $b/h=1$, the wake exhibits dual-frequency KH dynamics and develops a dual-row side-HV. Spanwise extension significantly enhances wake fluctuations. The turbulent kinetic energy is concentrated in regions of HV and side-HV formation, and is dominated by the streamwise component, with energy subsequently redistributed towards the vertical and spanwise components.

The flow normal to a stationary disk-like plate is investigated by direct numerical simulations across wide ranges of Reynolds number $Re$ ($100 \leq Re \leq 300$), number of polygon vertices $N$ ($2 \leq N \leq 5$), and compression ratio $k$ ($0 \leq k \leq 1$), where $k = 0$ and 1 correspond to a regular polygon and circular disk, respectively. All plates share identical area $A_r$ and diameter–thickness aspect ratio $\chi = D/t_d=50$, with the nominal characteristic diameter defined as $D = \sqrt {4A_r/\pi }$. Five flow regimes are observed for all disk-like plates, denoted as: (i) steady geometric-symmetric, (ii) steady reflectional-symmetric, (iii) reflectional symmetry breaking, (iv) reflectional symmetry-preserving (RSP), and (v) chaotic. The wake transition depends strongly on the number of vertices $N$, particularly for $N \leq 3$. For an elliptical plate ($N = 2$), the flow exhibits strong symmetry until it reaches the chaotic state. At $k=0.4$, an unusual RSP state is observed, characterised by periodic vortex shedding and a stable drag coefficient. Conversely, for triangular plates ($N = 3$), the wake possesses only weak symmetry, and once symmetry is broken, it never recovers; the RSP state is absent for all $k$ studies. For quadrilateral ($N = 4$) and pentagonal ($N = 5$) plates, the wake transition sequence encompasses all five flow regimes, closely resembling that of a circular disk, and providing a reference for polygonal plates of higher vertex count. The drag force exhibits a distinct parity effect: it oscillates at twice the shedding frequency for even-$N$ plates, but contains both the fundamental and harmonic frequencies for odd-$N$ plates. The compression ratio $k$ modulates the wake symmetry and transition. When the plate becomes nearly circular ($k=0.8$), the wake symmetry plane can deviate from the geometric symmetry plane of the plate. As $k$ increases, the geometry converges towards a circular disk, weakening the edge vortices and lowering the critical Reynolds numbers towards the disk values.

The spatial and temporal dynamics of separated flow induced by a fence with a splitter plate in uniform flow at moderate Reynolds numbers were investigated using time-resolved particle image velocimetry. The Reynolds numbers, based on the free-stream velocity and the fence height above the splitter plate, were 2700, 5500 and 7500. The mean separated flow is characterised by a large primary clockwise recirculating vortex above the splitter plate and a smaller counter-rotating secondary vortex in the corner of the fence and splitter plate. Guided by different vorticity thickness growth rates, the separated shear layer is partitioned into four regions, whose dynamics are governed by the initial roll-up, shear layer stabilisation, wall-induced large-scale vortex breakdown and post-reattachment recovery. Streamwise momentum transport, entrainment velocity, convective velocity, spectral proper orthogonal decomposition, as well as spatial autocorrelation and whole-field integral time scales are used to examine the dynamics of the shear layer across these four regions. Spectral analysis reveals a distinct frequency migration along the shear layer, wherein the Kelvin–Helmholtz frequency near the fence transitions to the vortex shedding frequency near reattachment through successive vortex pairing events. Analysis of instantaneous reverse flow areas demonstrates that the second half of the primary vortex dominates the global unsteadiness of the separation bubble, whereas the first half exhibits strong coupling between the primary and secondary vortices. Conditional averaging analysis indicates that flapping motion significantly modulates turbulence production, however, the dynamic importance of the mean velocity gradients and Reynolds stresses varies across the four regions.

The interaction between turbulent flows and bubbles is a complex phenomenon ubiquitous in natural and industrial settings. In this work, we experimentally investigate, from a fundamental perspective, the interaction between a rising bubble and a vortex ring in counterflow. Using time-resolved three-dimensional Lagrangian particle tracking (3D-LPT) coupled with shadowgraphy, we obtain simultaneous measurements of the bubble motion and the surrounding liquid flow. This approach enables detailed observation of bubble dynamics, deformation and eventual breakup, as well as the fluid motion. We examine several flow configurations by varying the vortex circulation and the Weber number while maintaining a comparable vortex-to-bubble size ratio. Based on these measurements, we classify the interaction events into three categories according to their impact on bubble dynamics and vortex stability over time. Through experiments, we address, for the first time, the three-dimensional effects of these interactions, which had not been considered in previous studies. The analysed experiments comprise the following: Case I, corresponding to a weak interaction in which neither the bubble nor the vortex is significantly affected; Case II, where the bubble is captured and advected by the vortex, leading to a strong distortion of the vortex due to the presence of the bubble within its core; and Case III, involving a stronger vortex capable of capturing the bubble and breaking it into two fragments without a severe loss of energy in the vortex core. The analysis of these results provides insight into the bubble breakup process and the mechanisms responsible for the destabilisation of the vortex ring.

We compare an inviscid vortex sheet model with continuous leading-edge shedding with direct Navier–Stokes simulations over a wide range of unsteady plate motions at moderate Reynolds number (${\textit{Re}} \approx 1000$). Approximately $70$ distinct kinematic configurations are examined, spanning both body-dominated and flow-dominated regimes. In body-dominated motions, where the fluid dynamics are primarily driven by prescribed plate accelerations, the inviscid model accurately reproduces normal force histories and the qualitative structure of the induced vorticity field. In flow-dominated configurations, with quasi-periodic vortex shedding, agreement with force predictions is good but reduced at low angles of attack, reflecting the greater sensitivity of vortex shedding dynamics to physical and computational parameters. The ability of the present formulation to accommodate stable, continuous leading-edge vortex shedding enables uniform comparisons across diverse motions and clarifies the regimes in which inviscid vortex sheet models can be used reliably for force prediction and physical interpretation.

Two distinct regimes arise during the early development of flow near the trailing edge of a flat plate impulsively started at small angles of attack. The first regime concerns the self-similar growth of a starting vortex at the edge; the second regime involves the advection of the starting vortex away from the edge, as described by Wagner’s classical model, which omits the first regime. In this work, we investigate the transition between these two regimes using a computational inviscid vortex-sheet method and an analytical point-vortex model. We show that this transition is triggered by vortex detachment, defined here as the instant at which two stagnation points on the plate surface annihilate each other and move off the plate. This vortex detachment is found to occur at the time, $t \approx 0.019 \, \alpha ^2 c/U$, where $\alpha$ is the angle of attack, $c$ is the plate chord and $U$ is the plate speed. We also demonstrate that this detachment process is independent of the angle of attack when the distance between the edge and the initial stagnation point is used as the characteristic length scale. These results provide insight into the early-time dynamics of vortex generation, motivating experimental validation and verification through numerical simulation of the Navier–Stokes equations.

The vortical structures in a flat-plate boundary layer disturbed by circular cylinder wakes are investigated using particle image velocimetry and hydrogen bubble visualization techniques. The cylinder diameter (D) and the gap between the cylinder and flat plate (G) are systematically varied to establish an investigated matrix of Reynolds number ReD = 530–1600, gap ratio $G/D$ = 0.33–6 and relative boundary layer thickness $\delta_0/D$ = 0.35–1.06 (δ0 is boundary layer thickness at the installation position of cylinder). An unexpected large critical value of $G/D$ = 4 is captured to divide the wake-vortices–boundary-layer interaction into two modes for $\delta_0/D$ = 1.06: the wake vortices trigger secondary vortices (SV) for $G/D$ ≤ 4; no secondary vortex is observed inside the boundary layer for $G/D$ > 4. The flow physics behind this mode switching is elaborated. An increase in $\delta_0/D$ is found to cause an earlier and stronger interaction for a fixed $G/D$. It is generally characterized by an earlier and faster growth of turbulent kinetic energy inside the boundary layer, stronger SV and a more pronounced deflection of wake vortex trajectories. The intensified interaction strengthens the mixing between the wake and boundary layer and accelerates the boundary layer transition, causing an earlier prevalence of hairpin vortex packets and a faster establishment of turbulent boundary layer. Although the interaction is simultaneously influenced by $G/D$ and $\delta_0/D$, the normalized growth rate of turbulent kinetic energy inside the boundary layer exhibits a remarkably exponential scaling with respect to $G/D$ during the initial stage of interaction.

We study the flow and drag generated by a perforated plate set in motion in a tow tank during the initial phases of its flow development over times less than that required to yield a fully developed wake. The effect of open area fraction on the vortex dynamics is investigated and found to cause a slow transition between a solid plate’s tight vortex-rollup behaviour and a highly perforated plate’s weak shear-layer behaviour. This change corresponds to suppression of the initial drag peak and subsequent drag undershoot of a solid plate. Paradoxically, this results in a region of time where adding perforation increases drag. We use our experimental data during the short acceleration period to close Inoue’s porous plate vortex model by leveraging a modification of small-time self-similar vortex dynamical theory introduced by Rott. We show that the results from Inoue’s model are useful in explaining many of the general aspects of the flow behaviour across all perforation levels tested, including the effect of perforation on force, circulation and vortex motion during and after the plate’s acceleration from rest.

The two-layer quasi-geostrophic (2LQG) model and the Eady model are two idealised systems illustrating the baroclinic instability of atmospheric jets and ocean currents. The two set-ups share many ingredients – background vertically sheared zonal flow of density-stratified fluid in a rapidly rotating frame – while differing in complexity and dimensionality. The Eady model has a continuous vertical direction, with baroclinic turbulence induced by boundary potential vorticity (PV) gradients at top and bottom. By contrast, the 2LQG sytem typically models baroclinic instability induced by interior PV gradients. This distinction challenges our ability to clearly identify a couple of ‘modes’ through which the Eady dynamics could be inferred from a simpler 2LQG system. In the present study, we show that this difficulty can be circumvented in the turbulent regime arising for weak bottom drag. Namely, guided by the common organisation of both systems into a gas of coherent vortices, we identify a quantitative mapping between the Eady and 2LQG models. The mapping allows for parameter-free predictions of the eddy diffusivity of the Eady model based on knowledge of the 2LQG diffusivity. We illustrate these results using numerical simulations of the Eady and 2LQG models with linear or quadratic bottom drag.

Systematic experimental data on local extreme velocities and unsteady features in high-Reynolds-number deep-cavity flows remain limited. In this study, two-component particle image velocimetry (PIV) measurements were performed to investigate the flow characteristics of an incoming-flow-driven deep cavity with $L/D$ = $1/3$ at Re = 2.55 × 105. Three streamwise $xy$ planes ($z/W$ = 0.10, 0.25, 0.50) and three spanwise yz planes ($x/L$ = 0.10, 0.25, 0.50) were measured systematically. The time-averaged velocity, root mean square velocity fluctuations, in-plane turbulent kinetic energy (TKE), instantaneous maximum velocity, and higher-order statistics including skewness and kurtosis were analysed. The results show that the vertical velocity fluctuation on the intermediate streamwise plane ($z/W$ = 0.25) reaches peak value approximately $v$rms/Ulid = 0.072 (where Ulid is the characteristic inflow velocity above the cavity), indicating the strongest local vertical unsteady response among the measured streamwise planes. On the near-wall plane ($z/W$ = 0.10), the instantaneous maximum velocity exhibits skewness 1.23 and kurtosis 7.47, reflecting pronounced local intermittent extreme events, whereas the extreme events on the middle plane ($z/W$ = 0.50) are weaker and closer to a Gaussian-like distribution. The spanwise planes also demonstrate clear non-Gaussian features, with high-fluctuation and high in-plane TKE regions primarily concentrated in areas associated with the interaction between the shear layer and recirculation structures, revealing significant spatial anisotropy in the flow. These results suggest that shear-layer development, primary recirculation, sidewall confinement and downstream flow turning jointly modulate local extreme events and intermittent velocity fluctuations. This study provides systematic experimental quantification of spatial non-uniformity and extreme-event characteristics in a high-Reynolds-number deep cavity using multi-plane PIV, offering useful experimental references for turbulence model validation and complex cavity-flow control.

We investigate the reconnection of two vortex bubble rings using direct numerical simulations of the incompressible two-phase Navier–Stokes equations with a volume-of-fluid method and a continuum surface force model. At fixed Reynolds number and varying Weber numbers ($\textit{We}$) spanning surface-tension-dominated to inertia-dominated regimes, the reconnection dynamics are divided into four stages, including approach, interfacial reconnection, helicity transport and pinch-off. Low $\textit{We}$ produces a larger reduction in interfacial area, leading to efficient reconnection and the formation of daughter bubbles. High $\textit{We}$ stretches the interface into slender filaments, producing residual fragments and secondary vortical structures. Simulations show that vorticity begins to rearrange towards the contact region before reconnection occurs, with surface tension modulating vorticity redistribution and interfacial contraction as $\textit{We}$ varies. These results relate $\textit{We}$ to interfacial morphology and the resulting reconnection topology, connecting vortex dynamics and interfacial physics in two-phase flows.

We investigate the interaction between vortex rings and cylindrical obstacles using direct numerical simulations across a wide range of geometric and dynamical parameters. The flow is characterised in terms of the diameter ratio between ring and object $T_D = d/D$, the Reynolds number based on circulation $\textit{Re}_\varGamma$, and the slenderness ratio $\varLambda$. By systematically varying $T_D$ and $\textit{Re}_\varGamma$, we identify three distinct interaction regimes: the wire, cutting and wall regimes. In the wire regime ($T_D \lesssim 0.05$), the primary vortex ring survives the interaction with limited deformation, and carries a weak lobe of secondary vorticity generated by the object’s boundary layer. As $T_D$ increases, the interaction transitions to the cutting regime, where the ring is split into two secondary structures formed through the reconnection between boundary-layer and ring vorticity. For sufficiently large obstacles ($T_D \gtrsim 0.8$), the wall regime emerges, in which boundary-layer vorticity dominates, and the primary ring is deflected and stretched along the obstacle surface. The transition between regimes depends primarily on $T_D$, while increasing $\textit{Re}_\varGamma$ enhances vortical dynamics, producing additional small-scale and tertiary structures. Finally, by modifying the topology of the obstacle, we demonstrate that reconnection and recovery of the primary ring depend critically on the topology of the secondary vorticity. These results provide a unified framework for interpreting vortex–body interactions, bridging the gap between vortex ring, tube and wall collision dynamics.

This study investigates the genesis and temporal evolution of turbulent eddies in violent-sloshing flows using a fully meshless computational framework. A quasi-Lagrangian $\delta$-large-eddy simulation–smoothed particle hydrodynamics formulation is employed to solve the weakly compressible Navier–Stokes equations, together with a novel methodology to quantify slosh-induced energy dissipation, where $\delta$ denotes the density-diffusion operator introduced in the $\delta$-SPH formulation. Under violent periodic forcing, the flow exhibits a strongly nonlinear free-surface dynamics, characterised by recurrent wave breaking and energetic impacts against the tank walls. By decomposing the total viscous dissipation into enstrophy-related and deformation-related contributions, we find that the enstrophy fraction remains nearly constant, at around $30\,\%$, across the investigated regimes. Moreover, in the absence of surface tension, the enstrophy-related dissipation does not converge under grid refinement; the inclusion of surface tension regularises this behaviour and promotes a shift of the vortex population towards larger coherent structures. High-resolution two-dimensional simulations, spanning a wide range of spatial resolutions, are complemented by fully three-dimensional simulations and by reduced-width three-dimensional configurations, in which the spanwise direction is fully resolved over a limited extent. This combined analysis shows that, for this class of bounded violent free-surface flows, global loads and energy dissipation are primarily governed by free-surface fragmentation and reconnection, rather than by fully three-dimensional turbulent cascade mechanisms. As a result, two-dimensional simulations provide an accurate description of the dynamics controlling the integral quantities of interest. These findings offer new physical insight into the coupling between free-surface fragmentation, vortex dynamics and dissipation mechanisms in violent sloshing, and establish a reference framework for future studies of turbulence generation in confined free-surface flows.

Micro-droplets are extensively used in chemical, biological and medical research, primarily for conducting various tests on samples, including living organisms, using a microfluidic framework. Recent studies have shown that the physiology of bacteria can be significantly altered when subjected to shear and/or extensional stresses. With this motivation, we perform experiments to understand the vortex dynamics involved during the pinch-off process in a cross-flow droplet generator, using particle image velocimetry to visualise the vortical structures and to quantitatively measure the associated stresses developed inside droplets. The process of pinching off inherently leads to bi-directional acceleration of fluid in the rapidly thinning capillary bridge, resulting in a vortex in the separated droplet as well as in the retracting ligament. We propose scaling laws for the vortical flow inside the droplet post pinch-off and predict the maximum circulation production inside the droplet. Further, we discuss the vortex dynamics inside the droplet, the retracting ligament and the advancing ligament and examine the stress fields associated with this transient phenomenon.

We study flapping foils at optimally propulsive Strouhal number $ \textit{St}=0.3$ with increasing chord-based Reynolds number $ \textit{Re} = 10^4$, $10^5$ and $10^6$ to examine changes in their unsteady boundary layers. Despite being prescribed the same freestream, the inner boundary-layer characteristics exhibit different trends due to the generation of leading-edge vortices (LEVs) and their advection into the downstream flow. Propulsive flapping foils show an extended laminar region known as the relaminarisation, during which the velocity profiles deviate from the standard log law. This relaminarisation is accompanied by a significant decrease in the cyclic fluctuation of the wall friction coefficient and an increase in the shape factor, while the freestream velocity increases under favourable pressure gradient conditions. This phenomenon intensifies with increasing $ \textit{Re}$. We found that higher $ \textit{Re}$ produces smaller LEVs in greater quantities, with a more rapid but stable breakdown, without resulting in a more chaotic turbulent downstream. This study strongly indicates that the relaminarization could extend beyond $ \textit{Re}=10^6$ as predicted by Fukagata et al. (2023 Annu. Rev. Fluid Mech., vol. 56, pp. 69–90). The results support the potential for further exploration of flapping foils at high $ \textit{Re}$ for noise and drag reduction.

This article presents results from an experimental, numerical and theoretical study of the short-wave instability of a helical vortex generated by a rotating blade. Experimental dye visualisations and corresponding numerical simulation show unstable displacement perturbations with wavelengths that are small compared with the helix radius and pitch, but can be large compared with the vortex core size. Stability analysis based on the experimental vortex profiles identifies large bands of unstable wavenumbers across different vortex bending modes, a result not compatible with existing theory on short-wave vortex instability. Similar modes are found for an array of straight vortices, showing that they are not related to vortex curvature. A theoretical analysis of the dispersion relation of Kelvin modes for the experimental vortex reveals the existence of a new family of modes, related to the specific vorticity profile of the vortex. Their non-resonant interaction via the strain field could explain the observed instability features.