Wave-assisted propulsion (WAP) systems directly convert wave energy into thrust using elastically mounted hydrofoils. The wave conditions as well as the design of the hydrofoil drive the fluid–structure interaction of the hydrofoil and, consequently, its performance. We employ simulations using a sharp-interface immersed boundary method to examine the effect of three key parameters on the flow physics, the fluid–structure interaction as well as thrust performance of these systems – the stiffness of the torsional spring, the location of the pitch axis and the Strouhal number. We demonstrate the utility of ‘maps’ of energy exchange between the flow and the hydrofoil system, as a way to understand and predict these characteristics. The force-partitioning method (FPM) is used to decompose the pressure forces into interpretable components and to quantify the mechanisms associated with thrust generation. Based on the results from FPM, a phenomenological model for the thrust generated by the WAP foil is presented. The parameters associated with this model are estimated based on data from over 450 distinct simulations. The predictions of the model are compared with the simulations and the use of this model for guiding WAP design is discussed.

Benthic macroalgae (including brown macroalgae or kelp) constitute one of the largest contributors to coastal primary production, but their ability to store and sequester carbon remains uncertain. Here, we use a numerical model of the flow/kelp interactions to study how tidal currents interact with an idealised numerical model of a giant kelp (Macrocystis pyrifera) forest, intending to better understand the potential for kelp growth in nutrient-limited conditions and the export of important tracers such as dissolved organic carbon. We calibrate and test our model using observations of currents within and surrounding a kelp forest in Southern California. By varying the density of kelp in our model, we find that there is a kelp density that maximises the export of tracer released from the kelp forest. Since the tracer advection/diffusion equation is linear with respect to the tracer concentration, the same kelp density corresponds to the maximum uptake for a tracer with a constant far-field concentration. The density at which this maximum occurs coincides with the density typical of natural kelp forests, where kelp growth may be limited by the uptake of dissolved nutrients from the surrounding water. Additionally, the drag induced on the tidal currents by the kelp forest results in a mean circulation through the kelp forest and a mean displacement of the kelp forest canopy.

A viscous, lubrication-like response can be triggered in a thin film of fluid squeezed between a rigid flat surface and the tip of an incoming projectile. We develop a scaling for this viscous approach stage of fluid-mediated normal impact, applicable to soft impactors. Under the assumption of mediating fluid being incompressible, the impacting solid displays two limit regimes: one dominated by elasticity, and the other by inertia. The transition between the two is predicted by a dimensionless parameter, which can be interpreted as the ratio between two time scales that are the time that it takes for the surface waves to warn the leading edge of the impactor of the forthcoming impact, and the characteristic duration of the final viscous phase of the approach. Additionally, we elucidate why nearly incompressible solids feature (a) substantial ‘gliding’ prior to contact at the transition between regimes, (b) the largest size of entrapped bubble between the deformed tip of the impactor and the flat surface, and (c) a sudden drop in entrapped bubble radius past the transition between regimes. Finally, we argue that the above time scale ratio (a dimensionless number) can govern the different dynamics reported experimentally for a fluid droplet as a function of its viscosity and surface tension.

Free transverse oscillations of an elastically mounted circular cylinder with low mass-damping are studied with a focus on the effects of the cylinder end condition on structural oscillations and vortex shedding. While the top end of the cylinder pierces the free surface of a water channel, the lower end is changed to have three end conditions: an attached endplate, an endplate unattached from the cylinder at varying gaps and no endplate. All three response branches are examined, with the reduced velocity sweeping $2 \le {U^\ast } \le 15$ (corresponding to a Reynolds number range of $2000 \le Re \le 14\;700$). Although the cylinder oscillations are unaffected by the end condition in the initial and upper branches, they show significant dependency on the end condition in the lower branch. When the endplate is attached or unattached with a small gap, the upper-to-lower branch transition occurs with a sudden decrease in oscillation amplitude, after which the lower branch maintains a near-constant amplitude. For larger gaps or no endplate, with increasing reduced velocity, the oscillation amplitude decreases gradually from its peak without any discernible sign of transition between the upper and lower branches. The three-dimensional effects of the gap are the basis for these differences in oscillation. Atop the strong tip vortex, a low-magnitude streamwise velocity region develops downstream of the cylinder, which delays upper-to-lower branch transition over the cylinder span that sees this low-velocity region. With increasing gap, this low-velocity region and the delay in transition spread over larger spanwise extents, forcing the overall body to oscillate at larger amplitudes.

The asymmetric instability in two streamwise orthogonal planes for three-dimensional flow-induced vibration (FIV) of an elastically mounted cube at a moderate Reynolds number of 300 is numerically investigated in this paper. The full-order computational fluid dynamics method, data-driven stability analysis via the eigensystem realization algorithm and the selective frequency damping method and total dynamic mode decomposition (TDMD) are applied here to explore this problem. Due to the unsteady non-axisymmetric wakefield formed for flow passing a stationary cube, the FIV response was found to exhibit separate structural stability and oscillations (including lock-in and galloping behaviour) in the two different streamwise orthogonal planes while the body is released. The initial kinetic energy accompanying the release of the cube could destabilize the above-mentioned structural stability. The observed FIV asymmetric instability is verified by the root trajectory of the structural mode obtained via data-driven stability analysis. The stability of the structural modes dominates regardless of whether the structural response oscillates significantly in various (reduced) velocity ranges. Further TDMD analysis on the wake structure, accompanied by the time–frequency spectrum of time-history structural displacements, suggested that the present FIV unit with galloping behaviour is dominated by the combination of the shifted base-flow mode, structure modes and several harmonics of the wake mode.

The present experimental study shows that a nozzle with optimal flexibility can enhance the impulse and entrainment of a pulsed jet. Near the nozzle exit, vortex rings emanating from the flexible nozzle move faster because of the timely release of the elastic energy (stored during the expansion) to the jet, which is maximized at the structural stiffness that needs to be optimally tuned to the jet acceleration. The total circulation, hydrodynamic impulse and entrained fluid volume are enhanced substantially. Interestingly, we find that the same condition for optimal flexibility to maximize the hydrodynamic impulse and circulation of the primary vortex ring of the continuous jet (Choi & Park, J. Fluid Mech., vol. 949, 2022, A39) holds universally for the pulsed jet, indicating that abrupt jet termination is irrelevant to the impulse augmentation mechanism. Compared to the rigid counterpart, increments of the impulse (${\sim }400\,\%$) and entrainment (${\sim }220\,\%$) of a pulsed jet in the present study are considerably larger than those ($200\,\%$ and $50\,\%$, respectively) in a continuous jet from previous studies, which is attributed to the significant suppression of negative pressure at the nozzle exit by the collapsing motion of the flexible nozzle in the phase with the jet-driven upstream propagation of the surface wave on the nozzle. This universal mechanism provides a guideline for a novel jet propulsor using a flexible nozzle, for example, for small-scale underwater robots.

Acoustic resonance is an important factor that contributes to aeroengine compressor failure. In this study, a plane cascade of compressor blades was designed to reproduce acoustic resonance via a low-speed wind tunnel test. A high-frequency hot-wire, microphone and strain gauge were used to synchronously measure the fluid, acoustic and structural parameters. We analysed the variation in the amplitude and frequency of the multi-field parameters with increasing mean flow velocity and explored the multi-field interaction mechanism that induces the acoustic resonance of the plane cascade. The plane cascade effectively reproduced the acoustic resonance phenomenon. The first-order acoustic-mode frequency of the plane cascade flow duct, second-order torsional vibration mode frequency of the blade and shedding mode frequency of the tip clearance leakage vortex were equal under acoustic resonance. The fluid, acoustic and structural fields showed a strong interaction effect, achieving the maximum blade vibration amplitude and causing fatigue cracks of torsional vibration at the blade root. The frequency lock-in region of the compressor plane cascade was divided into an ‘acoustic–structure’ interaction region, a ‘fluid–acoustic–structure’ interaction region and a first-order acoustic-mode dominant region with increasing mean flow velocity, which demonstrates an interesting phenomenon in which the fluid–acoustic–structure modes compete: acoustic mode > blade vibration mode > vortex shedding mode. The results demonstrate a unique approach to the study of acoustic resonance that provides insight into the acoustic resonance mechanism in a cascade of compressor blades.

We present evidence revealing that an object with specific properties can exhibit multiple stable falling postures at low Reynolds numbers. By scrutinizing the force equilibrium relationship of a fixed object at various attack angles and Reynolds numbers, we introduce a methodology that can obtain the stable falling postures of the object. This method saves computational resources and more intuitively presents the results in the full parameter domain. Our findings are substantiated by free-fall tests conducted through both physical experiments and numerical simulations, which validate the existence of multiple stable solutions in accordance with the interpolation results obtained with fixed objects. Additionally, we quantify the abundance and distribution patterns of stable falling postures for a diverse range of representative shapes. This discovery highlights the existence of multiple stable solutions that are universally present across objects of different shapes. The implications of this research extend to the design, stability control and trajectory prediction of all free and controlled flights in both air and water.

Previous work suggests that the arrangement of elements in an obstruction may influence the bulk flow velocity through the obstruction, but the physical mechanisms for this influence are not yet clear. This is the motivation for this study, where direct numerical simulation is used to investigate flow through an array of cylinders at a resolution sufficient to observe interactions between wakes of individual elements. The arrangement is altered by varying the gap ratio $G/d$ (1.2 – 18, G is the distance between two adjacent cylinders, d is the cylinder diameter), array-to-element diameter ratio $D/d$ (3.6 – 200, D is the array diameter), and incident flow angle ($0^{\circ} - 30^{\circ}$). Depending on the element arrangement, it is found that the average root-mean-square lift and drag coefficients can vary by an order of magnitude, whilst the average time-mean drag coefficient of individual cylinders ($\overline{C_{d}}$), and the bulk velocity are found to vary by up to $50\,\%$ and a factor of 2, respectively. These arrangement effects are a consequence of the variation in flow and drag characteristics of individual cylinders within the array. The arrangement effects become most critical in the intermediate range of flow blockage parameter $\mathit{\Gamma_{D}^{\prime}} = 0.5-1.5$ ($\mathit{\Gamma_{D}^{\prime}}=\overline{C_{d}}aD/(1-\phi)$, where a is frontal element area per unit volume, and $\phi$ is solid volume fraction), due to the high variability in element-scale flow characteristics. Across the full range of arrangements modelled, it is confirmed that the bulk velocity is governed by flow blockage parameter but only if the drag coefficient incorporates arrangement effects. Using these results, this paper proposes a framework for describing and predicting flow through an array across a variety of arrangements.

This study explores the dynamics of flexible ribbons with an added weight $G$ at the tail in uniform flow, considering key parameters like inflow Reynolds number ($Re_u$), mass ratio ($M_t$) and aspect ratio (${A{\kern-4pt}R}$). For two-dimensional ribbons, a simplified theoretical model accurately predicts equilibrium configurations and forces. Inspired by Barois & De Langre (J. Fluid Mech., vol. 735, 2013, R2), we introduce an important control parameter ($C_G$) that effectively collapses normalized forces and angle data. Vortex-induced vibration is observed, and Strouhal number ($St$) scaling laws with $C_G$ are identified. In three-dimensional scenarios, the model effectively predicts lift, but its accuracy in predicting drag is limited to situations with small $Re_u$ values. The flow along the side edges mitigates pressure differences, thereby suppressing vibration and uplift, particularly noticeable in the case of narrow ribbons. This study offers new insights into the dynamics of flexible bodies in uniform flow.

We use video footage of a water-tunnel experiment to construct a 2-D reduced-order model of the flapping dynamics of an inverted flag in uniform flow. The model is obtained as the reduced dynamics on a 2-D attracting spectral submanifold (SSM) that emanates from the two slowest modes of the unstable fixed point of the flag. Beyond an unstable fixed point and a limit cycle expected from observations, our SSM-reduced model also confirms the existence of two unstable fixed points for the flag, which were found by previous studies. Importantly, the model correctly reconstructs the dynamics from a small number of general trajectories and no further information on the system. In the chaotic flapping regime, we construct a 4-D SSM-reduced model that captures the system's chaotic attractor.

We investigate the three-dimensional (3-D) flow around and through a porous screen for various porosities at high Reynolds number $Re = {O}(10^4)$. Historically, the study of this problem has been focused on two-dimensional cases and for screens spanning completely or partially a channel. Since many recent problems have involved a porous object in a 3-D free flow, we present a 3-D model initially based on Koo & James (J. Fluid Mech., vol. 60, 1973, pp. 513–538) and Steiros & Hultmark (J. Fluid Mech., vol. 853, 2018 pp. 1–11) for screens of arbitrary shapes. In addition, we include an empirical viscous correction factor accounting for viscous effects in the vicinity of the screen. We characterize experimentally the aerodynamic drag coefficient for a porous square screen composed of fibres, immersed in a laminar air flow with various solidities and different angles of attack. We test various fibre diameters to explore the effect of the space between the pores on the drag force. Using PIV and hot wire probe measurements, we visualize the flow around and through the screen, and in particular measure the proportion of fluid that is deviated around the screen. The predictions from the model for drag coefficient, flow velocities and streamlines are in good agreement with our experimental results. In particular, we show that local viscous effects are important: at the same solidity and with the same air flow, the drag coefficient and the flow deviations strongly depend on the Reynolds number based on the fibre diameter. The model, taking into account 3-D effects and the shape of the porous screen, and including an empirical viscous correction factor that is valid for fibrous screens may have many applications including the prediction of water collection efficiency for fog harvesters.

Numerical simulations are carried out on the vortex-induced rotations of a freely rotatable rigid square cylinder in a two-dimensional uniform cross-flow. A range of Reynolds numbers between 40 and 150 and density ratios between 0.1 and 10 are considered. Results show eight different characteristic regimes, expanding the classification of Ryu & Iaccarino (J. Fluid Mech., vol. 813, 2017, pp. 482–507). New regimes include the transition and wavy rotation regimes; in the ${\rm \pi}$-limited oscillation regime we observe multipeak subregimes. Moment-generating mechanisms of these regimes and subregimes are further elucidated. A phenomenon related to the influence of density ratio is the tooth-like shape of the ${\rm \pi} /2$-limit oscillation regime observed in the regime map, which is explained as a result of the imbalance relation between the main frequencies of rotation response and the vortex shedding frequency. In addition, existence of multiple regimes and multistable states are discussed, indicating multiple stable attractive structures in phase space.

This work is a numerical and experimental study of a rectangular thin plate undergoing stall flutter at Mach 0.8. This constitutes one of the first studies of this kind where three-dimensionality is fully implemented in a numerical simulation including the test-section effects characterizing wind-tunnel experiments. In order to break down the fluid–structure interaction to its main driving phenomena, an aerodynamic model is proposed that is based on computationally inexpensive steady-state simulations. Two types of dynamic instability are observed in the numerical simulations; Flutter by mode coalescence is promoted at zero flow incidence, however, high bending precludes this from happening for higher values of angle of attack. Stall flutter is instead a nonlinear one-degree type of instability. Both of these instability mechanisms can be explained in terms of hysteretic behaviour of the pressure distribution, which becomes more pronounced at high angles of attack, when a large separation region is formed. Tests were conducted employing titanium alloy plates in order to survive the aerodynamic loads characterizing the wind-tunnel initial transient. However, due to wall interference, high bending was promoted so that the internal stress exceeded the yield values before flutter could be measured. Numerical simulations were in general agreement with the experiment in terms of both amplitude and oscillation frequency.

Compressible direct numerical simulations are employed to elucidate the low-wavenumber behaviour of wall-pressure fluctuations in turbulent channel flow and the effect of flow Mach number in the nearly incompressible regime. Simulations are conducted at bulk Mach numbers 0.4, 0.2 and 0.1, and friction Reynolds number 180. In addition to the convective ridge that is virtually Mach-number-independent, acoustic ridges, whose magnitudes are orders of magnitude lower, are identified in the two-dimensional wavenumber–frequency spectrum. At lower frequencies, the acoustic ridges represent propagating longitudinal and oblique waves that match the theoretical predictions of two-dimensional duct modes with a uniform mean flow. They decay with decreasing Mach number but remain distinctly identifiable even at Mach 0.1. At high frequencies, in contrast, no propagating waves are found, and the spectral level in the supersonic wavenumber range is broadly elevated and increases with decreasing Mach number.

Although poroelastic clusters in nature, such as bristled wings and plumed seeds, exhibit remarkable flight performances by virtue of their porous structure, the effects of another key feature, elasticity, on aerodynamic loading remain elusive. For a poroelastic cluster, we investigate the aerodynamic effects of elastic deformation that occurs through the collective rearrangement of many elastic components and the fluid-dynamic interactions between them. As a simple two-dimensional model, an array of multiple cylinders which are individually and elastically mounted is employed with diverse values of porosity and elasticity. Under a uniform free stream, the poroelastic cluster enlarges its frontal area and augments the total drag force in the quasi-steady state; this is in contrast to the general reconfiguration of fixed elastic structures, which tends to reduce the frontal area and drag. The rearrangement of the poroelastic cluster is dominated by the virtual fluid barrier that develops in a gap between the elastic components, interrupting the flow penetrating between them. The effects of this hydrodynamic blockage on changes in the frontal area and drag force are analysed in terms of porosity and elasticity, revealing the fluid-dynamic mechanism underlying the appearance of peak drag at an intermediate porosity. Moreover, to represent the coupled effects of porosity and elasticity on the rearrangement, a scaled elastic energy is derived through a consideration of the energy balance.

Flow within submerged canopies influences the transport of nutrients, sediment, pollutants, plant seeds and the settlement of larvae. To improve our understanding of mass transport within canopies, a simple model is proposed to predict the total time-varying velocity within submerged rigid canopies (representing coral reefs) and flexible canopies (representing seagrasses and saltmarshes). The model divides the momentum equations into a canopy layer and free-stream layer. The difference in the time derivative of the velocity between the two layers is balanced by the sum of the shear stress and canopy drag, both of which depend on the in-canopy total velocity. The present model extended the shear stress model developed for steady current to combined current and wave conditions without additional calibrating coefficients. The model agreed well with the in-canopy velocity measured in the present and several previous studies. Importantly, the proposed model significantly improved the accuracy of canopy time-mean velocity prediction, which reduced the root mean square error by more than 50 %, compared with previous models. The model revealed that the addition of waves can significantly decrease the in-canopy time-mean velocity.

Natural flyers and swimmers employ flexible wings or fins to propel. While the complex interaction between the foil with deformation and the surrounding non-steady fluid environment defines the propulsion performance of the propellers, elucidating the interaction mechanism through theoretical models earns much challenge. Based on elastokinetics and linear potential flow theory, this study proposes a simplified analytical model to clarify the kinematics and the propulsion performance of a flexible thin foil pitching in flow. The dynamical forces, including the inertial force of the foil and the non-steady fluid pressure, are used to determine the averaged deformation angle of the foil. Combining the averaged deformation angle and the prescribed driving pitching motion, the kinematics of the foil is resolved analytically. Based on the analytical expressions for the corresponding pitching motion, analytical relations among the physical parameters of the stiffness and the mass of the foil and the driving frequency are given to these critical conditions, including resonance of the flow–structure system, equal pitching amplitude between the flexible foil and the rigid counterpart, phase angle transition from ${\rm \pi}/2$ to $- {\rm \pi}/2$. Subsequently, the performance of the foil, including the thrust, the power and the propulsive efficiency, as a function of the flexibility of the foil are derived, together with the introduction of a bluff body type offset drag to the thrust. The formulated analytical theory, which matches nicely with previous reports, will help to interpret the effect of the flexibility and regulate the propulsive performance of the flexible foil when pitching in fluid.

A cylinder immersed in a current and free to translate along a circular arc is considered to investigate the impact of path curvature on the flow-induced vibrations (FIV) occurring without structural restoring force. Path curvature magnitude ($\kappa$, inverse of path radius non-dimensionalized by the body diameter $D$) is varied from $0$ (transverse rectilinear path) to $20$, over a wide range of values of the structure to displaced fluid mass ratio, $m^\star \in [0.05,10]$. The exploration is carried out numerically at subcritical and postcritical values of the Reynolds number ($Re$, based on $D$ and the inflow velocity), i.e. below and above the critical value $47$ for the onset of flow unsteadiness when the body is fixed, up to $100$. Path curvature triggers a desynchronized regime of the flow–body system in addition to the synchronized regime typical of vortex-induced vibrations, and alters the composition of fluid forcing. The most prominent effect uncovered here is, however, a global enhancement of FIV, with three principal results: (i) vibrations and flow unsteadiness are found to arise at lower subcritical $Re$ along a curved path, down to $19.5$ versus $31$ for $\kappa =0$; (ii) the $m^\star$ range where substantial responses develop is considerably extended and encompasses the entire interval under study, which contrasts with the narrow band of low $m^\star$ identified for $\kappa =0$; (iii) the vibrations are amplified, $+45\,\%$ relative to the peak amplitude measured along a rectilinear path at $Re =100$.

The stability and postcritical behaviour of a horizontal flag undergoing gravity-induced deformation and periodic contact with a nearby horizontal rigid wall are experimentally investigated. The results elucidate the combined effects of gravity and contact on flutter, and reveal design principles for application to triboelectric energy harvesting. By varying the free-stream velocity, flag thickness and distance between the flagpole and the wall, the dynamics of the flag are classified into quasistatic equilibrium, flutter, partial contact and saturated contact modes. Considering the significance of gravitational effects, a new dimensionless flow velocity is proposed to identify the distribution of the dynamic modes, and its definition varies according to whether the wall is placed above or below the flag. The critical conditions for transitions between the dynamic modes are determined from the balance of fluid dynamic and gravitational effects. The distance from the flagpole to the wall is found to be more critical for transitions in the lower-wall configuration than in the upper-wall configuration. The peak contact force as well as the oscillation amplitude and frequency at postequilibrium exhibits remarkably different trends depending on the location of the wall. The peak contact force imposed on the wall by the fluttering flag weakens as the distance to the wall increases in the case of an upper wall, whereas it becomes stronger in the case of a lower wall.