The hydrodynamics of vortex-induced vibration of a flexible pipe in bidirectionally sheared flows are investigated through combined experimental and numerical approaches. Such bidirectionally sheared flows are inspired by subsurface currents induced by internal solitons widely occurring in the ocean, which feature oppositely directed flow velocities along the flexible pipe. Experiments are conducted in an ocean basin using a tensioned pipe with distributed strain sensors, and numerical simulations are conducted by a validated strip method based framework. The mean in-line displacement, mean drag, shear force and bending moment are characterised. The mean in-line displacement, maximised over the spanwise direction, exhibits an approximately quadratic dependence on the maximum velocity in bidirectionally sheared flow. In contrast, the mean drag coefficient remains nearly unchanged with increasing flow velocity. Both trends are cross-validated via experiments and simulations. Furthermore, empirical expressions are proposed to describe the influence of background flow velocities on the shear force and bending moment. Excitation and added mass coefficients associated with dominant frequency response and time-varying hydrodynamic coefficients considering multi-frequency responses are extracted and analysed. The results show that the phase difference between the cross-flow and in-line responses retains an antisymmetric distribution, whereas the excitation coefficients exhibit quasi-symmetric patterns around the mid-span. The time-dependent added mass coefficient is strongly correlated with the wake pattern, with negative values occurring predominantly during P + S and 2P vortex shedding patterns. Moreover, spectral proper orthogonal decomposition is employed to link the dominant vortex-induced vibration frequencies of the flexible pipe with the surrounding flow field. The results indicate a clear transition in which the dominant flow field frequency follows the Strouhal frequency at lower velocity, but aligns with the structural vibration frequency at higher velocity associated with the occurrence of the lock-in phenomenon.

This study investigates the influence of a rear-attached splitter plate on the vortex dynamics and turbulence characteristics in the wake of a circular cylinder. Three-dimensional direct numerical simulations (DNS) are performed at a turbulent Reynolds number of 1000 and non-dimensional plate lengths ($ L/D$) of 0–4. The splitter plate affects the vortex dynamics and turbulence characteristics in a highly non-monotonic manner. Specifically, both the strength of the primary vortices and the turbulent kinetic energy in the wake decrease with increasing $ L/D$ over $ L/D$ = 0–1.5, followed by a local increase over $ L/D$ = 1.5–2 and another decrease over $ L/D$ ≥ 2. The abnormal local increase is because the vortex formation location transitions from downstream of the splitter plate for $ L/D$ ≤ 1.5 to the two sides of the plate for $ L/D$ ≥ 2. Owing to the presence of the primary vortex street in the wake, the turbulence in the wake is strongly anisotropic both globally and locally. After removing the contribution from the coherent primary vortices, the wake becomes much more isotropic globally and homogeneous locally. The present DNS dataset also enables an evaluation of several widely used surrogate models for the kinetic energy dissipation rate. A major finding is that a minor increase in the contribution of the coherent component (e.g. for $ L/D$ ≥ 2) may strongly deteriorate the applicability of the surrogate models of local axisymmetry and local homogeneity. In general, this study provides new insights and mechanisms for the control of turbulence in bluff-body wakes.

The wake systems of a conventional ducted propeller ($\mathrm{DP}$) and a rim driven thruster ($\mathrm{RDT}$) are compared. The latter is an innovative ducted propeller, whose blades are installed on a rim rotating within the nozzle, with their tips oriented inwards and no need of a rotating hub. The flow was reproduced by large eddy simulation (LES) on a cylindrical grid consisting of 6.3 billion points. Substantial deviations between the flow physics downstream of the two propellers are revealed and an order of magnitude drop in the pressure minima and turbulent stresses is found across the rotor and in the wake of $\mathrm{RDT}$. These changes are mainly attributable to the absence of the hub vortex, the helical vortices from the root of the blades, and the leakage flow generated between their tip and the inner surface of the nozzle. In the rim driven thruster, they are replaced by inner, helical vortices shed from the tip of its blades. In addition, the trailing wake of the blades of $\mathrm{RDT}$ is populated by smaller streamwise vortices and lower turbulence levels. This is due to their modified design, characterised by a more uniform spanwise distribution of the load, allowed by the absence of both the hub and the leakage between the tip of the blades and the nozzle. In conventional ducted propellers, they require a reduction of the load of the blades towards their root and their tip with the purpose of mitigating the intensity of the hub vortex and the leakage flow, respectively.

Velocity measurement techniques, such as particle image velocimetry (PIV), face a trade-off between field of view, spatial resolution and sampling rate, so that small-scale vortices, shear layers and high-frequency turbulent motions are often under-resolved. Most physics-informed reconstructions use a velocity–pressure formulation, even though pressure is not measured in typical PIV experiments, so the Navier–Stokes constraints are only weakly enforced. We address this issue by formulating a vorticity–velocity physics-informed network (VVPINN), in which pressure is eliminated and incompressibility is enforced together with a vorticity transport equation, thereby directly constraining the velocity field and its derivatives. We then compare this formulation with a conventional velocity–pressure PINN (VPPINN) for spatio-temporal super-resolution of planar PIV data in three cases: a laminar multi-cylinder wake, a two-dimensional Taylor–Green vortex and an experimental two-cylinder wake. In the Taylor–Green vortex case, with identical architectures and training strategies, the VVPINN yields smaller velocity errors, reduces the $L_2$ errors in vorticity and shear by approximately $10\,\%$, and the pressure gradient errors by up to approximately $30\,\%$ at moderate super-resolution factors, and produces instantaneous fields with more physically plausible vorticity, shear and fine-scale pressure gradient patterns. Spectral analysis shows that the temporal energy spectrum is recovered accurately, whereas the wavenumber spectra, particularly beyond the Nyquist wavenumber, remain more difficult to match because the training data strongly constrain the time histories at sampled locations, but only indirectly inform the smallest spatial scales. Overall, the results indicate that vorticity-based constraints provide a more effective route to physics-consistent super-resolution of sub-sampled PIV data than the conventional velocity–pressure formulation.

Quantifying the contribution of vortex structures to wall forces is essential for identifying the primary sources of forces. The traditional force-element method focuses on the contribution of flow structures to the resultant force. However, the contribution of flow structures to the distributed force cannot be identified. This work proposes a distributed force element method to address this issue. Inspired by the framework of matched asymptotic expansions, the method resolves the surface pressure by matching the fundamental solutions of the outer wave and inner flow regions. The pressure is thus decomposed into contributions from a convective acceleration term, a boundary acceleration term and a boundary vorticity term. The method is implemented by solving the resulting linear system with singular value decomposition. The volume source is further decomposed into direct radiation and boundary scattering components. It is found that compared with the direct radiation component, the boundary scatter component decays fast in the wake. Consequently, the direct radiation component is dominant in the far wake. A finite-domain pressure correction is proposed based on the direct radiation component. The distributed force element method is validated using several benchmark cases: two-dimensional configurations including laminar flow around stationary and oscillating circular cylinders; three-dimensional cases comprising laminar flow past a sphere, subcritical flow past a sphere and laminar flow over an inclined spheroid. The results suggest that the proposed distributed force element method enables the precise quantification of how flow structures in the wake and around the bluff bodies contribute to the surface pressure.

The present study establishes a general theory for fluid-element rotation and intrinsic vorticity decompositions within the framework of vorticity kinematics. We propose two direction-dependent vorticity decompositions (DVDs) based on the analysis of rotation of directed material line and surface elements, with the rigid-rotation and spin modes of vorticity being explicitly defined. Intrinsic coupling relations are then derived for a pair of orthogonal line and surface elements, demonstrating their complementary roles in both kinematics and geometry. Notably, the surface-element-based spin mode is shown to coincide with the relative vorticity in the generalized Caswell formula, thereby providing a faithful representation of surface shear stress in Newtonian fluids. Correspondingly, another two DVDs are constructed based on the geometry of streamlines and streamsurfaces in the field description. Furthermore, within the characteristic algebraic description, in terms of the rotational invariants $(\psi ,\gamma )$ in the real Schur form of the velocity gradient tensor, two invariant vorticity decompositions (IVDs) are formulated. The first IVD with positive spin aligns with the Liutex-shear decomposition, which corresponds to the Klein–Kaden–Betz (KKB) mechanism by which wrapping shear layers form axial vortices. The second IVD is indispensable for understanding unidirectional swirling motion around a point on the rotation-axis-normal plane ${\mathcal{P}}$, corresponding to an anti-KKB mechanism/phenomenon characterized by the negative spin. Importantly, it is proved that the DVD vorticity modes are rigorously bounded by the IVD vorticity modes $(R_{N}^{\pm },s_{N}^{\pm })=(2\psi ^{\pm },\gamma ^{\pm })$ on ${\mathcal{P}}$. Finally, distinctive features and applicability of these kinematic tools are demonstrated with representative examples. The results indicate that a coupled IVD–DVD approach provides a powerful diagnostic tool for unravelling the subtle structures and fundamental physics inherent to complex flow fields.

This paper investigates the mean flow asymmetry about the meridional plane in crossflow over a 6 : 1 prolate spheroid using high-fidelity numerical simulations. A series of direct numerical simulations are performed at diameter-based Reynolds number $\textit{Re}_{\!D} = 3.0 \times 10^3$ over a range of angles of attack. We identify a critical angle of attack for the onset of mean flow asymmetry between $40^\circ$ and $42^\circ$. In cases where asymmetry eventually develops, the flow initially remains symmetric for an extended period before turbulent fluctuations in the wake perturb the symmetry. As wake turbulence becomes more vigorous at higher Reynolds numbers, this observation suggests a reduced critical angle of attack – an expectation confirmed by simulations at $\textit{Re}_{\!D} = 6.0 \times 10^3$. To investigate the mechanism responsible for the asymmetry, we propose a new measure of mean asymmetry and derive a corresponding transport equation from the Navier–Stokes equations. This formulation identifies the production and destruction terms governing the evolution of asymmetry. Our analysis of the equation reveals that the generation mechanism is primarily inviscid, suggesting that the findings at low Reynolds number may extend to higher Reynolds numbers. Finally, we present spectral analyses of the force and moment histories at $45^\circ$ angle of attack, revealing two dominant frequencies and their physical origin, and quantifying inter-scale interactions by applying amplitude modulation analysis to the force and moment signals.

This paper investigates the physical origins of pressure fluctuations on the stationary shroud wall of a mixed-flow pump. A novel ‘triple source model’ is developed and applied to experimental validated stress-blended eddy simulations. The model decomposes stationary-frame pressure fluctuations into three distinct rotating-frame components to disentangle complex tip leakage vortex (TLV) interactions: (i) kinematic ‘non-uniform fluctuation’ ($p_{\textit{NUF}}$) from the steady blade sweep, (ii) dynamic ‘flow synchronous fluctuation’ ($p_{\textit{FSF}}$) phase-locked to rotation, and (iii) ‘flow asynchronous fluctuation’ ($p_{\textit{FAF}}$) from all non-phase-locked phenomena. Analysis reveals that shroud unsteadiness is over 90 % dominated by the synchronous components along the TLV trajectory. Crucially, the model uncovers a counter-intuitive destructive interference mechanism between the kinematic sweep $p_{\textit{NUF}}$ and the dynamic response $p_{\textit{FSF}}$, with local cross-correlation coefficient –0.26, explaining how dynamic instabilities can dampen the steady pressure footprint. Source-term analysis of the pressure Poisson equation establishes a complete causal chain from specific velocity field interactions to pressure signatures: (i) the non-uniform fluctuation is kinematically driven by the mean momentum flux from blade loading, contributing 52.27 % to the local pressure asymmetry; (ii) the flow synchronous fluctuation is generated by periodic vortex–turbulence interaction, contributing 80.22 % of its total source; (iii) and the asynchronous broadband pressure is sourced from the canonical turbulent cascade, contributing 79.33 % of its total source. Spatial correlations confirm the TLV as the common physical nexus for all components. This work establishes a quantitative diagnostic framework that moves beyond qualitative vortex observation, providing a physical basis for the targeted mitigation of turbomachinery unsteadiness.

This study uncovers a striking similarity between massively separated laminar and turbulent flows that develop over a square wing during extreme vortex gust encounters. The evolving large-scale, vortical core structures responsible for significant transient lift variations exhibit remarkable similarity across ${\textit{Re}}=600$ and 10 000. The formation of these structures is attributed to a substantial gust-induced vorticity flux produced at the wing surface, resulting in shared large-scale topological features between the low- and high-Reynolds-number flows. Although fine-scale vortical structures quickly emerge in the ${\textit{Re}}=$ 10 000 case, the large-scale structures identified by scale decomposition of the turbulent flow resemble those observed at ${\textit{Re}}=600$. These findings suggest that large-scale vortical features present in laminar extreme aerodynamic flows provide key insights into their higher Reynolds number counterparts, potentially reducing the complexity of flow modelling and control for extreme aerodynamics.

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.

Vortical flows over spinning cones with half-angles of $\theta _c =$ $10^\circ$, $15^\circ$, $22.5^\circ$, $30^\circ$ and $45^\circ$ at incidence angles of $\alpha$ between 0$^\circ$ and 36$^\circ$ are experimentally studied employing smoke streak flow visualisation and planar particle image velocimetry at Reynolds numbers of $\mathcal{O}(10^4)$ and base rotational speed ratios between 0 and 3. Symmetric vortex triads are observed on the leeward side of the stationary cones at incidence that grow in cross-section and strength along the surface. Spin breaks down this symmetry. Asymmetries in the vortex systems over the spinning cones are characterised by anti-cyclonic vortices forming in the counter-rotating meridian and cyclonic vortices in the co-rotating meridian. The anti-cyclonic vortices increase in strength as they are pushed in the direction of rotation and embrace the surface of the cone, whereas cyclonic vortices detach from the surface and exhibit unchanging vortex strength. For the most slender cone of $\theta _c = 10^\circ$, the cyclonic vortices are pushed past the plane of symmetry into the counter-rotating meridian and are squeezed between the anti-cyclonic vortex and the surface of the cone. This appears to trigger the detachment of the anti-cyclonic vortices. The thickest cone of $\theta _c = 45^\circ$ exhibits characteristics similar to flows over a disc (Kuraan & Savaş J. Visual. vol. 23, 2024, pp. 191–205), a limiting case of the cone family. As $\alpha$ increases, the stagnation point departs from the vertex and monotonically shifts along the windward surface. Regular vortex shedding events in the wake region behind the $\theta _c=45^\circ$ cone are detected in the streakline images, also a common characteristic of flows over discs. Wave patterns are observed near the leeward surface of spinning cones, which are likely signatures of the well-known centrifugal spiral wave instabilities. The bead-like features leave small-scale wave patterns on detached portions of the neighbouring trailing vortices. Inclined wave patterns form on streaklines over the entire surface of the cones, and are present in both non-spinning and spinning cases; hence, they are likely signatures of classical cross-flow boundary layer instabilities.

The vertical, tip-to-tip arrangement of neighbouring caudal fins, common in densely packed fish schools, has received much less attention than staggered or side-by-side pairings. We explore this configuration using a canonical system of two trapezoidal panels (aspect ratio ${\textit{AR}}=1.2$) that pitch about their leading edges while heaving harmonically at a Strouhal number $St=0.45$ and a reduced frequency $k=2.09$. Direct numerical simulations based on an immersed-boundary method are conducted over a Reynolds-number range of $600\leq {\textit{Re}}\leq 1\times 10^{4}$, and complementary water-channel experiments extend this range to $1\times 10^{4} \leq {\textit{Re}}\leq 3\times 10^{4}$. Results indicate that when the panels oscillate in phase at a non-dimensional vertical spacing $H/c\leq 1.0$ with $c$ denoting the panel chord length, the cycle-averaged thrust of each panel rises by up to 14.5 % relative to an isolated panel; the enhancement decreases monotonically as the spacing increases. Anti-phase motion instead lowers the power consumption by up to 6 %, with only a modest thrust penalty, providing an alternative interaction regime. Flow visualisation shows that in-phase kinematics accelerate the stream between the panels, intensifying the adjacent leading-edge vortices. Downstream, the initially separate vortex rings merge into a single, larger ring that is strongly compressed in the spanwise direction; this wake compression correlates with the measured thrust gain. The interaction mechanism and its quantitative benefits persist throughout the entire numerical and experimental Reynolds-number sweep, indicating weak ${\textit{Re}}$-sensitivity within $600\leq {\textit{Re}}\leq 3\times 10^{4}$, and across multi-panel systems. These results provide the first three-dimensional characterisation of tip-to-tip flapping-panel interactions, establish scaling trends with spacing and phase, and offer a reference data set for reduced-order models of vertically stacked propulsors.

Many species of fish, as well as biorobotic underwater vehicles (BUVs), employ body–caudal fin (BCF) propulsion, in which a wave-like body motion culminates in high-amplitude caudal fin oscillations to generate thrust. This study uses high-fidelity simulations of a mackerel-inspired caudal fin swimmer across a wide range of Reynolds and Strouhal numbers to analyse the relationship between swimming kinematics and hydrodynamic forces. Central to this work is the derivation and use of a model for the leading-edge vortex (LEV) on the caudal fin. This vortex dominates the thrust production from the fin and the LEV model forms the basis for the derivation of scaling laws grounded in flow physics. Scaling laws are derived for thrust, power, efficiency, cost-of-transport and swimming speed, and are parametrised using data from high-fidelity simulations. These laws are validated against published simulation and experimental data, revealing several new kinematic and morphometric parameters that critically influence hydrodynamic performance. The results provide a mechanistic framework for understanding thrust generation, optimising swimming performance, and assessing the effects of scale and morphology in aquatic locomotion of both fish and BUVs.

We investigate the interaction between two equally signed neutral vortices, namely vortices with a vanishing area integral of vorticity in inviscid non–divergent two-dimensional flows or a vanishing volume integral of potential vorticity anomaly in three-dimensional quasi-geostrophic (QG) flows. The vortices have a continuous (potential) vorticity distribution, and are linear combinations of appropriately normalised cylindrical (or spherical) Bessel functions of order 0, truncated at a zero of the Bessel function of order 1. Some pairs of neutral vortices reach an oscillating near-equilibrium state, attracting and repelling each other as a result of the exchange of small amounts of vorticity in their peripheries. This vorticity exchange generates a dipolar moment within each vortex which separates the vortices slightly, whereas the subsequent radial redistribution of the vorticity causes the vortices to come back closer again. The interaction is slower and weaker in three-dimensional QG flows, as the potential vorticity exchange primarily takes place close to the horizontal mid-plane of the vortices. These results have been corroborated using two radically different numerical models, namely a pseudo-spectral model and a high-resolution contour-advection model, both in two and in three dimensions. The observed oscillation mechanism could explain the persistence of geophysical vortices under the influence of other vortices and their ability to form stable vortex structures without experiencing vortex merging.

Results of an experimental study investigating issues of Coriolis effects on the fluid dynamics associated with vortex rings propagating through a rotating fluid are presented. The vortex rings are generated at the top of a large, water-filled rotating tank and they propagate downwards along the axis of rotation. The motion and the decay of the rings in a rotating fluid are expected to be accompanied by an inertial-wave field being established in the fluid surrounding the rings. However, the existence of this inertial-wave field had previously never been verified experimentally. Particle image velocimetry measurements were performed with the goal of demonstrating the existence of the inertial-wave field. Datasets were processed to extract individual inertial-wave modes and, for the first time, experimentally construct the dispersion relation for the inertial waves associated with vortex rings. For rotation rates when Coriolis forces dominate the dynamics, the experimental data are found to be in very good agreement with the well-established theoretical dispersion relation for inertial waves. The generation of inertial waves implies that kinetic energy is radiated away from the vortex rings. First results relating to the redistribution process of the kinetic energy are briefly discussed.

Unsteadiness lies at the heart of turbulent fluid dynamics, eddy formation and instabilities in flows, thus making it central to both understanding and controlling fluid systems. In this work, we present an objective measure for the unsteadiness of a time-dependent velocity field, the deformation unsteadiness, derived from a spatio-temporal variational principle, allowing for a frame-independent assessment of the unsteadiness of a given flow field. Additionally, as an application of our main result, we define an objective analogue of the classical $Q$-criterion based on extremisers of unsteadiness minimisation. We apply our results to several examples of analytical flows as well as simulated flow data sets in two and three dimensions. In particular, we apply our newly derived vortex criterion to several explicit, time-dependent solutions of the Navier–Stokes equation and compare the results with existing vortex criteria. We give a physical interpretation of the deformation unsteadiness and discuss future research directions.

We investigate two-dimensional vortex merging of three vortices, initially aligned and evenly spaced, with the two outer vortices having the same strength and the middle one having any strength. Based on the vorticity transport equation (VTE) a vortex is identified as an extremum of the vorticity. The vorticity is also investigated through the low-dimensional core-growth model, providing analytical insight into the vorticity patterns and transitions, including explicit formulas of trajectories of the critical points of vorticity. Four distinct vorticity patterns and four types of trajectories of the vorticity are found. For a corotating centre vortex there are two types of trajectories of the vorticity, one where the centre vortex dominates the two outer vortices, and one where the centre vortex is suppressed by the two outer vortices. The two types of trajectories are separated in parameter space by the strength ratio of the inner to outer vortex being $4\exp (-{3}/{2})$. In the case of a counter-rotating vortex centre, the centre vortex is suppressed in the flow transitions for centre vortex strengths less than the sum of the two outer vortices. For a range of vortex strengths of the middle vortex, the three vortex configuration first rotates in one direction and then shifts direction of rotation. In the case of a centre vortex strength exceeding the sum of the two outer vortices, the two outer vortices are pushed away. The core-growth model quantitatively reproduces the VTE flow for low Reynolds number (Re) and topologically provides accurate descriptions up to Re = 1290 where filamentation vortices are created.

This paper reports analytical solutions for steadily travelling two-dimensional water waves on deep water, without gravity or surface tension, carrying a cotravelling periodic row of hollow vortices. The solutions are hollow-vortex regularisations of the exact solutions of Crowdy & Roenby (Fluid Dyn. Res., vol. 46, 2014, 031424) for the analogous waves carrying a submerged point-vortex row, the free-surface shapes of which coincide with those for pure capillary waves and, like those, exhibit steady pinchoff at a critical wave amplitude. The same pinchoff phenomenon is shown to occur for the hollow-vortex regularisations. The new wave solutions are likely to provide a useful basis for perturbative, asymptotic or numerical studies when additional effects such as gravity, capillarity or compressibility are incorporated.

In this study, we investigate the dynamic behaviour of reconfigurable circular plates under acceleration as a model problem to understand the interplay between kinematics and shape deformation in biological propulsion. A high-resolution force transducer and time-resolved particle image velocimetry were employed to simultaneously capture both hydrodynamic forces and vortex dynamics. The results reveal that, unlike rigid plates that exhibit Reynolds number independence, the force evolution of reconfigurable plates is governed by the dimensionless bending stiffness ${\textit{EI}}^*$. A distinct load-shifting phenomenon is observed – characterized by a reduction in peak force amplitude and an elevation of the postpeak force trough, contrasting with the ‘peak-valley’ behaviour typical of rigid plates. Based on ${\textit{EI}}^*$, reconfigurable plates are classified into three regimes: extra-flexible (${\textit{EI}}^* \lt 2.28 \times 10^{-3}$), flexible ($2.28 \times 10^{-3} \leqslant {\textit{EI}}^* \leqslant 0.143$) and rigid (${\textit{EI}}^* \gt 0.143$). Notably, only plates within the flexible regime exhibit the load-shifting phenomenon. Flow visualizations show that the flexible plates, due to their shape reconfiguration, produce flow fields with two distinct features: initially, the formation of three-dimensional, non-axisymmetric vortex rings; subsequently, vortex breakdown occurs due to instability. By applying the vorticity moment theorem, force generation is accurately estimated from the flow field. Using a vortex-based low-order force model, the radial distribution of vorticity is identified as the key mechanism underlying the load-shifting phenomenon. This finding suggests that biological morphing structures in real propulsion scenarios can reduce force fluctuations without compromising average thrust by ‘load-shifting’, offering insights into efficient propulsion strategies.

This study investigates finite-wall effects in vortex ring–wall interactions on flat circular plates with diameters $1.5D_n \leqslant D \leqslant 10D_n$, where $D_n$ is the nozzle diameter. Flow visualisation experiments were conducted across a broad range of vortex Reynolds numbers, ${\textit{Re}}_{\varGamma } \approx 600$–$2800$, while particle image velocimetry measurements were performed over a focused range of ${\textit{Re}}_{\varGamma } \approx 1300$–$1900$. The formation length was fixed at $L/D_n = 2$, where $L$ is the length of the ejected fluid slug. The plate sizes examined span from those reproducing the canonical infinite-wall behaviour to plates smaller than the vortex ring’s diameter. Three distinct regimes are identified based on the relative plate size: (i) ‘infinite’ plates where edge effects are negligible; (ii) ‘quasi-infinite’ plates where boundary-layer separation dominates but weak edge-generated vorticity emerges; and (iii) ‘finite’ plates where boundary-layer roll-up over the edge replaces surface separation, yielding strong edge effects. These regimes are established through vorticity contour analysis and flow visualisation, supported by quantitative measurements of circulation, trajectory, vortex-core velocity, eccentricity and boundary-layer separation. Within the explored range, geometric extent rather than Reynolds number governs the interaction dynamics. Finite-edge effects manifest through enhanced and earlier secondary vorticity formation, stronger primary vortex decay and elongated rebound trajectories with larger orbital periods. When the plate diameter becomes smaller than the vortex ring diameter, edge clipping rapidly disrupts the coherent vortex structures. The results provide a canonical framework for understanding finite-surface interactions and for distinguishing edge-induced dynamics from curvature or confinement effects observed in previous studies.