This study examines the cross-flow vortex-induced vibration (VIV) of a circular cylinder in combined current–oscillatory inflows, revealing a distinct multi-frequency response characterised by beat-like modulation. Systematic water-channel experiments were conducted across a range of reduced velocities, inflow oscillation intensities and frequency ratios to investigate the synchronisation mechanisms among inflow velocity variations, cylinder motion and hydrodynamic loading. Results show that the presence of oscillatory inflow can lead to significant deviations of vibration amplitudes from quasi-steady predictions within the upper-branch regime. At a given reduced velocity, the cylinder motion is dominated by a primary frequency component similar to that observed in steady flow, but accompanied by two secondary components. The contributions of these supplementary frequencies increase with inflow oscillation intensity but diminish as the oscillation frequency rises. Analysis of time-varying hydrodynamic forces reveals that, in the upper-branch regime, the vortex-force phase angle deviates substantially from quasi-steady estimation based on instantaneous reduced velocity, which is associated with non-quasi-steady vortex-shedding patterns. Particle image velocimetry measurements reveal that when the minimum vortex-force phase angle lies between 0$^\circ$ and 180$^\circ$ over the inflow oscillation cycle, a mixed vortex-shedding mode emerges. This mode is characterised by a vortex sequence resembling the ‘2P’ (two-pair) shedding pattern but with negligible secondary vortices, occurring predominantly during intervals of low inflow velocity. A theoretical framework incorporating nonlinear damping and excitation coefficients assuming quasi-steady response well predicts VIV amplitudes and elucidates the influence of inflow oscillation intensity and frequency on the emergence of supplementary vibration frequencies.

The present work numerically investigates the dynamics of inclined thin flexible plates in oscillatory flows to assess the effects of bending stiffness, wave orbital excursion and inclination angle on plate deflection, reconfiguration, drag force and energy conversion. Four distinct structural response modes are identified, together with their transition conditions. An analytical expression for the lift coefficient of inclined rigid plates in the oscillatory flow is derived. By combining the drag and lift coefficients, we propose a modified Cauchy number, which quantitatively reveals the inclination effect from both geometric and mechanical perspectives. The dynamic behaviours of the plate deflection can be separated into two states. In the fully reconfigured state, a balance is achieved between elastic restoring force and hydrodynamics-driven force. Based on moment and energy balance, we derive a scaling law incorporating the modified Cauchy number, which accurately predicts the variation of tip deflection. In the passive movement state, the flexible plate moves passively along the flow, and its tip deflection saturates to the order of wave orbital excursions. A pronounced drag reduction is induced by the plate reconfiguration, following a $-1$ scaling law with a combined parameter, which is explained by the model of effective plate length. The energy conversion from fluid kinetic energy to structural elastic strain energy first increases and then decreases with increasing flexibility, yielding an optimal energy conversion efficiency. The modified Cauchy-number-based scaling law accurately predicts the averaged elastic energy growth and critical conditions for optimal energy conversion through a time scale competition mechanism.

The vortex-induced vibration of multiple spring-mounted bodies free to move in the orthogonal direction of the flow is investigated. In a first step, we derive a linear arbitrary Lagrangian–Eulerian method to solve the fluid–structure linear problem as well as a forced problem where a harmonic motion of the bodies is imposed. We then propose a low computational-cost impedance-based criterion to predict the instability thresholds. A global stability analysis of the fluid–structure system is then performed for a tandem of cylinders and the instability thresholds obtained are found to be in perfect agreement with the predictions of the impedance-based criterion. An extensive parametric study is then performed for a tandem of cylinders and the effects of mass, damping and spacing between the bodies are investigated. Finally we also apply the impedance-based method to a three-body system to show its validity to a higher number of bodies.

The propulsion of a flapping wing or foil is emblematic of bird flight and fish swimming. Previous studies have identified hallmarks of the propulsive dynamics that have been attributed to unsteady effects such as the formation and shedding of edge vortices and wing–vortex interactions. Here, we show that several key features of heaving flight are captured by a quasi-steady aerodynamic model that aims to predict stroke-averaged forces from wing motions without explicitly solving for the flows. We address the forward dynamics induced by up-and-down heaving motions of a thin plate with a nonlinear model which involves lift and drag forces that vary with speed and attack angle. Simulations reproduce the well-known transition for increasing Reynolds number from a stationary state to a propulsive state, where the latter is characterised by a Strouhal number that is conserved across broad ranges of parameters. Parametric, sensitivity and stability analyses provide physical interpretations for these results and show the importance of accounting for the flow regimes which are demarcated by Reynolds number and angle of attack. These findings extend the phenomena of unsteady locomotion that can be explained by quasi-steady modelling, and they broaden the conditions and parameter ranges over which such models are applicable.

Experimental investigation is presented to elucidate flow structures and corresponding frequencies on finite span, cantilevered wings as functions of sweep angle and taper ratio. A detailed parameters sweep of planform geometry varied the leading and trailing edge sweep angles of NACA 0015 wings with a semi-aspect ratio of 2. The experiments were performed at Reynolds numbers O($10^5$) and angles of attack $12^\circ$–$22^\circ$. The experiments included flow visualisations, volumetric flow measurements, time-resolved measurements at selected spanwise planes and aerodynamic loads. This is the first time, to the best knowledge of the authors, that multiple configurations were tested under the same exact conditions. The correlation between three-dimensional (3-D) Reynolds stress distributions and 3-D flow separation is presented. Moreover, spectral content reveals modes that vary along the span, as well as for different planforms. For all wings, at the locations of largest reversed flow, power spectral density (PSD) peaks were seen at $0.1\lt St\lt 0.2$, corresponding to vortex shedding. At spanwise locations near surface spirals the PSD exhibits peaks at lower frequencies of St = O(0.01) due to focus point wandering. The mean flow fields presented here show similarities to previous numerical simulation findings on similar geometries at Reynolds number O($10^2$). Moreover, the spanwise location of the largest magnitude of turbulent kinetic energy corresponds to the location of the most amplified mode at a Reynolds number of 400 found previously. The present research, complemented by previous low-Reynolds-number work, provides fundamental insights into global flow structures on multiple finite span wings, their corresponding spectral content and the effect on their aerodynamic performance.

The effects of section shape, specifically thickness and camber, on the lift spectrum for a foil immersed in a turbulent flow are analytically and experimentally investigated. The lift response functions to incident cross-stream vortices drifting along streamlines offset from the foil within two chord lengths are computed using an analytical solution to the Blasius force equation, achieved by way of using an expanded Joukowsky mapping function that can map a circle in the complex plane to any selected foil shape. The vortex lift responses are convolved with the vorticity wavenumber–frequency spectrum for a homogenous turbulent flow to compute the overall foil lift due to incident turbulence. Calculations of the lift spectra for a series of foils with increasing maximum thickness, NACA 651A-0008, -0012 and -0016 foils, immersed in grid-generated turbulent flow agree very well with measurements up to the maximum measured frequency, $\omega C/2U \approx 40$, where $C$ is the chord and $U$ is the free-stream speed, which showed an increasing level of lift attenuation at high frequencies with increasing foil thickness. The analytical model showed that the high-frequency lift was controlled by the inertia of the incident vortices, and that the thickness of the foil near the leading-edge controls these high-frequency lift levels by decreasing the drift velocities of the approaching vortices. A simplified analytical model of the vortex inertia force, which avoided the need to implement the unsteady Kutta condition, was developed to estimate the high-frequency lift for thick foils with less computational demand. A wind tunnel experiment involving unsteady lift measurements for a foil in a turbulent flow was performed to physically confirm the model-based prediction that increasing the foil leading-edge thickness can significantly attenuate high-frequency lift, while maintaining the overall maximum thickness. Undesired components of the unsteady force measurements associated with foil vibration were removed using a novel technique of analysing measured force spectra over a series of wind tunnel speeds. The unsteady lift spectra measured for a NACA 0007-61 foil, modified to have constant thickness from 10 % to 50 % chord, showed an approximate attenuation of 8–10 decibels at reduced frequency, $\omega C/2U = 30$, relative to a NACA 0007-65 foil, which agreed well with the model-based predictions and confirmed that increasing the foil thickness in the vicinity of the leading edge yields significant high-frequency lift attenuation.

Understanding fluid-elastic instabilities in slender bodies is crucial for predicting and controlling flow-induced vibration (FIV) in engineering and biological systems. The FIV of a prolate spheroid with an aspect ratio of $\epsilon = 3$, a mass ratio of $m^* = 3$ and a damping ratio of $\zeta = 0$, elastically mounted in a uniform flow at ${\textit{Re}} = 600$, are investigated using direct numerical simulations and a reduced-order model (ROM). As reduced velocity $U_r$ increases, five vibration states emerge: quasi-steady (QS), periodic (PM), large-amplitude chaotic (LAC), quasi-periodic (QP) and small-amplitude chaotic (SAC) modes. These mode regimes form two categories of response branches, namely synchronised branches (SB) and desynchronised branches (DB). In SB, three synchronisation mechanisms are identified, i.e. conventional lock-in (CLI), secondary-component lock-in (SCLI) and superharmonic lock-in (SHLI), corresponding to PM, LAC and QP modes, respectively. In contrast, DB comprises two types. The flow-dominated desynchronised (FDD) branch corresponds to QS mode, where flow instability dominates while structural vibrations remain weak. The dual-mode competition desynchronised (DMCD) branch corresponds to the SAC mode, where fluid and structural instabilities coexist but fail to synchronise. Analysis of wake dynamics identifies spanwise, transverse and high-frequency spanwise shedding patterns that are closely correlated with vibration regimes. The overlap of the response branches produces three distinct hysteresis zones, emphasising the sensitivity of spheroidal FIV to initial conditions and its inherently path-dependent behaviour. Dynamic mode decomposition (DMD) and an ERA-based ROM, which together resolve mode-specific spatial structures and frequency evolution, show that the vibration dynamics is governed by a persistently unstable wake mode (WM) and a structural mode (SM) whose stability alternates across branches. This clarifies the resulting sequence of vibration modes and provides insight into how different branches compete and transition.

Understanding the vortex interactions and wake transitions for flapping flexible foils is important because of their increased usage in bioinspired aquatic and aerial robotic propulsors. Although wake transitions have been studied for rigid foils, we experimentally investigate how flexibility alters the transitions and vortex interactions for flexible foils, which are closer to the natural flapping foils in fish, birds and insects. We conduct the experiments in a flowing soap film on a pitching airfoil with a flexible filament at its trailing edge (TE). We find that, apart from the Strouhal number (${\textit{St}}$), flexural rigidity (${\textit{EI}}$) is important to determine the transitions. We vary ${\textit{EI}}$ of the flexible filament by three orders of magnitude and also investigate an extreme case of ${\textit{EI}} \rightarrow \infty$. Flexibility triggers the shedding of multiple small ‘secondary vortices’ (SVs) along with big ‘primary vortices’ (PVs), unlike only PVs for the rigid foil. Continuous deformations of the flexible filament play crucial roles in determining the interaction of boundary layer vortices and trailing edge vortices and, ultimately, the generation and evolution of PVs and SVs. We identify five vortex interaction mechanisms (VIMs). Depending on how SVs interact with PVs, the wake assumes different patterns. We construct the ${\textit{St}}$–${\textit{EI}}$ phase maps for wake transitions and newly identified VIMs. We devise a non-dimensional parameter $\varUpsilon$, referred to as ‘Yashavant number’. One order increase in $\varUpsilon$ reduces the number of VIMs by one. Instead of following the usual transition route, the flexible foil reveals counterintuitive transition trends that strongly depend on the filament ${\textit{EI}}$.

Flexible substrates are effective in suppressing splashing, but they simultaneously lead to inhibition of spreading (Howland et al. 2016 Phys. Rev. Lett. vol. 117, 184502; Vasileiou et al. 2016 Proc. Natl Acad. Sci. USA vol. 113, pp. 13307−13312). In addition, there has been limited investigation and no established scaling law for the splashing threshold in the case of flexible substrates. To address these points, this paper proposes a lotus-leaf-like disk that can effectively suppress droplet splashing without inhibiting the maximum spreading of droplets. This situation is numerically studied in this paper. Five dynamic modes of the impacting droplet are identified with various Weber numbers (defined as the inertia force relative to the surface tension force) and different disk’s stiffnesses. The threshold Weber number of splashing is developed by considering the flexibility of substrates. Finally, the results demonstrate that the proposed method not only suppresses the splashing but also maintains the maximum spreading.

A coupled computational-fluid-dynamics/finite-element methodology is implemented to investigate the free aerodynamic separation of clusters of equally sized spheres arranged in regular configurations in Mach-20 flow, representing an idealized meteoroid-fragmentation scenario. The regular nature of the initial agglomeration geometries – touching sphere pairs, tetrahedral four-sphere arrangements and face-centred-cubic 13-sphere configurations – allows a systematic exploration of both individual sphere motions and bulk cluster dynamics as the initial orientation is varied. For sphere pairs, a stable lifting configuration arises when the spheres are in contact in a skewed configuration, a phenomenon that can also emerge in the more populous clusters. In the tetrahedral survey, comprising 38 initial orientations, shock surfing of downstream bodies is found to play a significant role in driving the separation dynamics. Despite substantial variations in detailed sphere motions with initial orientation, the trajectory type and final lateral velocity collapse reasonably well with the initial polar angle of the sphere within the cluster. Indices describing the bluntness and asymmetry of the initial configuration are introduced and correlate well with the collective cluster dynamics, though not always in an intuitive way. For the 13-sphere clusters, the dependency of individual sphere lateral velocities follows a similar trend with initial polar angle to the four-sphere case, suggesting that a simplified separation model may be possible for such configurations. The influence of the initial cluster bluntness on the bulk dynamics is somewhat reduced, however, indicating a tendency towards more homogeneous separation as the cluster population is increased.

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.

The hydrodynamic performance of oscillating elastic plates with tapered and uniform thickness in an incompressible Newtonian fluid at varying Reynolds numbers is investigated numerically using a fully coupled fluid–structure interaction computational model. By leveraging the acoustic black hole effect, tapered plates can generate bending patterns that vary from standing wave to travelling wave oscillations, whereas plates with uniform thickness are limited to standing wave oscillations. Simulations reveal that although both standing and traveling wave oscillation modes can produce high thrust, travelling waves achieve significantly higher hydrodynamic efficiency, and this advantage is more pronounced at higher Reynolds numbers. Furthermore, regardless of the oscillation mode, tapering leads to greater hydrodynamic performance. The enhanced hydrodynamic efficiency of travelling wave propulsion is associated with the reduced amount of vorticity generated by tapered plates, while maintaining high tip displacements. The results have implications for the development of highly efficient biomimetic robotic swimmers, and more generally, the better understanding of the undulatory aquatic locomotion.

Predicting unsteady loads on plate-like objects during unsteady motion is important in many applications, such as ship manoeuvring, flight and biological propulsion. The drag force on a starting plate that moves normal to its surface can be severely underestimated during the acceleration phase when conventional methods are used to incorporate the effects of acceleration. These methods often introduce an inviscid added mass force that has its origin in potential flow. However, the flow field around a starting plate quickly diverges from potential flow after the start of the motion due to the continuous creation of vorticity at the plate surface. Following the concept of drag by Burgers (1921 Proc. K. Ned. Akad. Wet. 23, 774–782), we propose a model to predict the creation of vorticity on the plate surface and its advection into the vortex loop at the plate edges, based on Stokes’ first problem. This model shows that the acceleration drag force is a history force, in contrast to the inviscid added mass force that is proportional to the instantaneous acceleration of the plate. We perform experiments on starting plates over a large range of accelerations, velocities, fluid viscosities and plate geometries for which the model gives accurate predictions for the drag force during acceleration and during the relaxation phase immediately after the acceleration ceases. This model is extended to also predict the drag forces on accelerating plates during a starting motion with a non-constant acceleration.

The dynamics of a fluid flow about its limit cycle can be analysed through phase reduction analysis – an approach that distils a high-dimensional dynamical system to its scalar phase dynamics. This technique provides insights into phase sensitivity, revealing the mechanisms that advance or delay phase dynamics. The phase-based reduced-order model derived from this approach serves as a foundation for identifying lock-on conditions and designing flow control techniques. Recent work by Sumanasiri et al. (J. Fluid Mech. vol. 1020, 2025, R4) applied phase reduction analysis to the fluid–structure interaction problem of aerofoil flutter in a free stream. Their analysis systematically changed the stiffness of the structural dynamics to decipher the phase dynamics mechanism of flutter. Moreover, they considered the use of optimised heaving motion to suppress the emergence of flutter. Their approach opens new avenues for modifying flow physics through innovative modifications of material properties and structural dynamics.

Dense arrays of soft hair-like structures protruding from surfaces are ubiquitous in living systems. Fluid flows can easily deform these soft hairs, which in turn impacts the flow properties. At the microscale, flows are often confined, which exacerbates this feedback loop: the hair deformation strongly affects the flow geometry. Here, I investigate experimentally and theoretically pressure-driven flows in laminar channels obstructed by a dense array of elastic fibres or ‘hairs’. I show that the system displays a nonlinear hydraulic resistance that I model by treating the hair bed as a deformable porous medium whose height results from the deflection of individual fibres. This fluid–structure interaction model encompassing flow in porous media, confinement and elasticity is then leveraged to identify the key dimensionless parameter governing the problem: $\hat {f}_0$, a dimensionless drag that combines fluid, solid and geometrical properties. Finally, I demonstrate how these results can be harnessed to design passive flow control elements for microfluidic networks.

Fully resolved three-dimensional simulations of planar gravity currents are conducted to investigate the influence of imposed spanwise perturbations on flow evolution and mixing at two Reynolds numbers ($ \textit{Re}=3450$ and 10 000). The initial perturbations consist of sinusoidal waves with a varying number of repeating waves, $k_y$, with simulations spanning $0 \leqslant k_y \leqslant 8$. At low-$ \textit{Re} $, cases with perturbations ($k_y \gt 0$) exhibit a more rapid breakdown of spanwise coherence compared with the unperturbed case ($k_y = 0$), although the resulting structures retain spatial periodicity and remain relatively ordered. This earlier disruption leads to greater front propagation distances beyond the self-similar inertial phase compared with the unperturbed case. Notably, imposed perturbations exhibit minimal influence on the flow transition; all cases follow the slumping velocity reported in the literature, with the transition into the inertial phase occurring at comparable times across different $k_y$ values at both $ \textit{Re} $. The increased propagation speed is accompanied by reduced mixing efficiency due to the premature disruption of coherent Kelvin–Helmholtz (K–H) billows, which play a key role in maintaining multi-scale mixing. At high-$ \textit{Re} $, the influence of initial spanwise perturbations diminishes, as three-dimensional turbulence induces a more chaotic, fine-scale breakdown of spanwise coherence across all $k_y$ cases, overriding the effects of the initial perturbations. Consequently, the dominant stirring mechanism shifts from K–H billows to vortices within the current head. Nevertheless, the unperturbed case maintains comparatively higher mixing efficiency at both low- and high-$ \textit{Re} $. This is attributed to the persistence of recognisable K–H billow structures, which, despite undergoing chaotic breakdown at high-$ \textit{Re} $, still contribute to effective stirring by stretching and folding the density interface. These results highlight the dual role of K–H billows: they promote efficient mixing, yet the enhanced mixing reduces the density difference between the current and the ambient fluid, weakening buoyancy and slowing front propagation despite stronger stirring. These findings are supported by consistent trends in streamwise density distribution and ‘local’ energy exchange analyses.

The stability of free jets is one of the fundamental problems that has driven the development of new theoretical and numerical methods in fluid mechanics. Extensive research has focused on the convective instabilities that characterise their elusive dynamics. However, in real-world configurations, free jets are often confined by solid walls which may exhibit different degrees of flexibility. The present paper presents, for the first time, evidence that even slightly flexible nozzles can lead to global instabilities. To show it, we adopted the classical tools of linear stability analysis, solving the fluid–structure interaction (FSI) problem by an arbitrary Lagrangian–Eulerian method, formulating a monolithic three-field problem. The investigation of the base flow properties reveals the effect of the Reynolds number, based on the bulk velocity and channel height, in the range $[50,200]$ and of the plate stiffness on the nozzle deformation and on the jet flow development. Exploiting an idea first proposed by Luchini and Charru, we develop an ad hoc quasi-one-dimensional model capable of predicting the displacement of elastic boundaries even for large displacements. The stability and sensitivity analysis shows that the interaction of the flow with the flexible structure leads to two categories of globally unstable modes: sinuous (in-phase) modes and varicose (out-of-phase) modes. All the results presented have been cross-checked with direct numerical simulations of the nonlinear FSI system, revealing that the instabilities correspond to supercritical bifurcations. This work has significant implications for many natural and industrial phenomena where a jet is produced by a compliant nozzle.

This paper investigates the aerodynamic and flow characteristics of a circular cylinder near the leading-edge separated flow of an elongated rectangular cylinder. The study varies the gap-to-diameter ratio (G/D) of 0 ≤ G/D ≤ 0.4 and distance-to-diameter ratio (L / D) of 0.6 ≤ L / D ≤ 5.8 in the subcritical Reynolds-number region. Here, D, G and L are the diameter of the circular cylinder, the gap between the two isomeric cylinders and the distance between the leading edge of the rectangular cylinder and the centre of the circular cylinder, respectively. Based on smoke-wire flow visualisations, particle image velocimetry test results, lift power spectral densities and pressure distributions, flow around the circular cylinder can be classified into three regimes, i.e. broadened body, body reattachment and co-shedding. In the broadened-body regime, gap flow is negligible, and the circular cylinder behaves as an extension of the rectangular cylinder. In the body-reattachment regime, the free shear layer separated from the rectangular cylinder’s leading edge reattaches to the circular cylinder forebody, significantly modifying its incoming flow. In the co-shedding regime, the free shear layer substantially alters the vortex shedding from the circular cylinder’s lower side, resulting in a distorted alternating vortex shedding from the circular cylinder. Both the drag and lift of the circular cylinder display distinct behaviours in the three flow regimes. Two primary flow modes are recognised through proper orthogonal decomposition analysis: an alternating vortex shedding mode and a one-sided shear flow mode, which result in two Strouhal numbers of 0.205 and 0.255, respectively.

We investigate the unsteady lift response of compliant membrane wings in hovering kinematics by combining analytical inviscid theory with experimental results. An unsteady aerodynamic model is derived for a compliant thin aerofoil immersed in incompressible inviscid flow of variable free-stream velocity at high angles of attack. The model, representing a spanwise section of a hovering membrane wing, assumes small membrane deformation and attached flow. These assumptions are supported by experiments showing that passive membrane deformation suppresses flow separation when hovering at angles of attack up to $55^\circ$. An analytically derived expression is obtained for the unsteady lift response, incorporating the classical Wagner and Theodorsen functions and the membrane dynamic response. This theoretical expression is validated against experimental water-tank measurements that are performed on hovering membrane wings at angles of attack of $35^\circ$ and $55^\circ$. Data from membrane deformation measurements is applied to the theoretical lift expression, providing the theoretical lift response prediction for each of the available experimental scenarios. Results of the comparison show that the proposed theory accurately predicts unsteady lift contributions from membrane deformation at high angles of attack, provided the deformation remains small and the flow is attached. This agreement between inviscid theory and experimental measurements suggests that when flow separation is suppressed, the unsteady aerodynamic theory is valid well beyond the typical low-angle-of-attack regime.

This study presents an active flow control framework for fluid–structure interaction (FSI) systems involving a flexible plate in the wake of a cylinder, by integrating Koopman-based reduced-order models (ROMs) with model predictive control (MPC). Specifically, a novel switched-system control strategy is developed, wherein kernel dynamic mode decomposition (DMD) and residual DMD are jointly employed to construct accurate ROMs capable of capturing strongly nonlinear FSI dynamics. This approach ensures accurate low-order representations across multiple control inputs, while suppressing spurious modes. The resulting Koopman ROMs provide fast state predictions over a receding horizon, enabling an MPC optimiser to determine real-time actuation. To improve control performance, resolvent analysis is utilised to optimise the actuator–probe placement. Remarkably, only three strategically placed structural probes are sufficient to capture dominant Koopman modes and enable effective closed-loop control. The proposed framework is then applied to regulate synthetic jets on the cylinder to suppress the plate’s flapping. It successfully stabilises large-amplitude (LAF), small-deflection (SDF) and small-amplitude (SAF) flapping regimes within a unified control strategy. By combining Koopman modal decomposition with an analysis of system energy evolution, we elucidate distinct control mechanisms across these regimes. For LAF and SAF cases, control is achieved primarily through local modulation of existing saturated modes, which requires relatively low actuation energy. In contrast, stabilisation of the SDF case involves the emergence of entirely new Koopman modes that disrupt the original symmetry-breaking dynamics, resulting in increased control input. The framework matches the control performance of reinforcement learning while markedly reducing computational cost.