Torsional vibration and galloping of a triangular prism (TP) in steady flow is investigated numerically at mass ratio 2.5, low Reynolds number 150, three angles of attack, and reduced velocities up to 40. The vibration of the TP is torsional galloping characterised by monotonic increase of the angular amplitude with the increase of reduced velocity. The angular displacement and amplitude are non-dimensionalised by 2π/3, which is the geometrical period in the rotation direction. The response of the TP is well correlated to the direction of the fluid moment coefficient on a stationary TP with a constant rotation angle. The rotation angles are consistently divided into excitation and damping ranges where the directions of the mean fluid moment of a stationary TP and the rotational angle are the same, and opposite to each other, respectively. When the reduced velocity is less than a critical value, the vibration amplitude falls into a damping range, and it increases with the increase of reduced velocity. When the reduced velocity is greater than this critical value, the galloping of the TP is strong and very aperiodic. The vibration amplitude switches very frequently between multiple amplitudes. Every identified amplitude is very close to the upper boundary of a damping range. Multiple-amplitude torsional galloping is a distinct feature that was not found in transverse galloping in the crossflow direction.

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 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.

This study examines how wavy orientation and undulation-induced geometric variations regulate vortex formation, wake transitions and aerodynamic performance in sinusoidally wavy cylinders. Using three-dimensional (3-D) simulations at a Reynolds number Re = 100, we analyse the transition from two-dimensional (2-D) to 3-D wakes across varying spanwise wavelengths and undulation configurations. A novel framework is introduced for classifying vortex structures, analyisng centreline trajectories and decomposing vortex structures, revealing how geometric variations induce distinct 3-D vortical structures. At short wavelengths, vortices originate from bluff regions and diminish in a continuous manner, stabilising the wake. At longer wavelengths, phase-dependent vortex onset leads to localised interactions, disrupting wake coherence and delaying stabilisation. A key discovery is the role of transverse recirculating flow in wake stabilisation, which induces reverse impingement, redirects fluid and weakens spanwise vortex coherence. Additionally, wavy orientation strongly influences vortex evolution and dislocation, altering vortex trajectories and wake stability. To further clarify these wake transitions, a classification framework is introduced, defining distinct phases such as vortex stretching, break-up and re-symmetrisation. The relationship between force characteristics and wake stabilisation is also established, with wavy orientation and undulation geometry regulating the transition from quasi-2-D spanwise vortical flow to 3-D spiral flow. A critical wavelength is identified where drag and lift fluctuations are minimised, with elliptical-section undulations achieving superior aerodynamic performance through enhanced vortex synchronisation. These findings provide new insights into vortex control strategies, with applications in bio-inspired propulsion, passive flow control and energy-efficient aerodynamic designs across engineering and industrial fields.

We numerically study the flow past an azimuthally oscillating cylinder at Reynolds number ${\textit{Re}}=250$ to analyse the three-dimensionalities observed in the recent experiments of Bhattacharyya et al. (J. Fluid Mech., vol. 950, 2022, p. A10). Specifically, we focus on the two newly discovered three-dimensional instability modes, referred to as modes Z and Y in the experiments, by suitably varying the cylinder oscillation amplitude and forcing frequency. Our direct numerical simulations (DNS) visually confirm the unique honeycomb-like structure of mode Y, also matching its spanwise wavelength, while mode Z, also referred to as mode D elsewhere, is not found at the expected parametric space but at an oscillation amplitude three times higher. Spectral proper orthogonal decomposition modes extracted from the DNS data reveal the near-wake dynamics of mode Y to be modulated by the forcing frequency and its subharmonics. Mode D/Z is found to be strongly correlated with a two-dimensional modal regime, especially at the forcing frequency, its subharmonic and higher harmonics. Mode Y does not show significant correlations with this two-dimensional flow except at a low frequency and only at its far wake. The honeycomb nature of mode Y is a result of its relatively higher forcing frequency causing multiple vortex sheddings over a rather compact space. Higher cylinder oscillation amplitude increases the overall drag, with the two-dimensional flow regimes generally yielding lower drag and lift. The results here suggest mode Y to be a unique three-dimensional mode of azimuthally oscillating cylinders and mode D/Z to be merely an intermediate state with the cylinder wake transitioning from the classical three-dimensional mode B to a two-dimensional state.

The two-dimensional to three-dimensional wake transition of a circular cylinder in a sinusoidal oscillatory flow arises from the Honji instability at a critical Keulegan–Carpenter number (denoted $\textit{KC}_{cr}$) with a corresponding critical spanwise wavelength (denoted $\lambda _{cr}$) for a given Stokes number (denoted $\beta$) larger than approximately 50. However, significant discrepancies in the $\textit{KC}_{cr}$ and $\lambda _{cr}$ values exist among the theoretical predictions by Hall (J. Fluid Mech., vol. 146, 1984, pp. 347–367), empirical formulae by Sarpkaya (J. Fluid Mech., vol. 457, 2002, pp. 157–180) and other experimental and numerical results in the literature. These long-standing discrepancies are addressed in this study, and new equations for $\textit{KC}_{cr}$ and $\lambda _{cr}$ are proposed for $\beta = 55$–$10^{6}$. The present $\textit{KC}_{cr}$ and $\lambda _{cr}$ values agree well with the Floquet analysis results of Elston et al. (J. Fluid Mech., vol. 550, 2006, pp. 359–389) for $\beta \sim 50$–$100$, and asymptotically converge to theoretical predictions by Hall (1984) as $\beta \to \infty$, but deviate significantly from the empirical formulae by Sarpkaya (2002). The underlying physical mechanisms for these deviations are elucidated. In addition, we reproduce the quasi-coherent structure (QCS) numerically for the first time, and demonstrate that the QCS observed by Sarpkaya (2002), where transient Honji vortices become pronounced near peak flow velocities but diminish during deceleration, is physically induced by ambient disturbances inevitably contained in physical experiments, such that $\textit{KC}_{cr}$ given by Sarpkaya (2002) is specific to the level of disturbance in his experimental setting and is somewhat arbitrary.

The interaction of an object with an unsteady flow is non-trivial and is still far from being fully understood. When an aerofoil or hydrofoil, for example, undergoes time-dependent motion, nonlinear flow phenomena such as dynamic stall can emerge. The present work experimentally investigates the interaction between a hydrofoil and surface gravity waves. The waves impose periodic fluctuations of the velocity magnitude and orientation, causing a steadily translating hydrofoil to be susceptible to dynamic stall at large wave forcing amplitudes. Simultaneous measurement of both the forces acting on the hydrofoil and the flow around it by means of particle image velocimetry (PIV) are performed, to properly characterise the hydrofoil–wave interaction. In an attempt at alleviating the impact of the flow unsteadiness via passive flow control, a bio-inspired tubercle geometry is applied along the hydrofoil leading edge. This geometry is known to delay stall in steady cases but has scarcely been studied in unsteady flow conditions. The vortex structures associated with dynamic stall are identified, and their trajectories, dimension and strength characterised. This analysis is performed for both straight- and tubercled-leading-edge geometries, with tubercles found to qualitatively modify the flow behaviour during dynamic stall. In contrast to previous studies, direct measurements of lift do not evidence any strong modification by tubercles. Drag-driven horizontal force fluctuations, however, which have not previously been measured in this context, are found to be strongly attenuated. This decrease is quantified and a physical model based on the flow observations is finally proposed.

A linear theory for unsteady aerodynamic effects of the actuator line method (ALM) is developed. This theory is validated using two-dimensional ALM simulations, where we compute the unsteady lift generated by the plunging and pitching motion of a thin aerofoil in uniform flow, comparing the results with Theodorsen’s theory. This comparison elucidates the underlying characteristics and limitations of ALM when applied to unsteady aerodynamics. Numerical simulations were conducted across a range of chord lengths and oscillation frequencies. Comparison of ALM results with theoretical predictions shows consistent accuracy, with all Gaussian parameter choices yielding accurate results at low reduced frequencies. Furthermore, the study indicates that selecting a width parameter ratio of $\varepsilon /c$ (the Gaussian width parameter over the chord length) between 0.33 and 0.4 in ALM yields the closest alignment with analytical results across a broader frequency range. Additionally, a proper definition of angle of attack for a pitching aerofoil is shown to be important for accurate computations. These findings offer valuable guidance for the application of ALM in unsteady aerodynamics and aeroelasticity.

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.

The dual-tone transition phenomenon and its formation mechanism in the flow around a heptagonal cylinder (side number $N= 7$) are experimentally investigated in depth over a range of free-stream velocities corresponding to Reynolds numbers of the order of $10^4$–$10^5$. Dual tone in this context refers to the emergence of two dominant peaks in the far-field acoustic spectrum when a flow in transition regime passes over a polygonal cylinder in principal orientations. The dual-tone phenomenon is also observed in an $N = 9$ cylinder in the face orientation and an $N = 11$ in the corner orientation, which contrasts with all the other polygonal cylinders of $N\in {\mathbb{Z}}[3,12]$ systematically investigated in the present study, where only a single tonal peak dominates the spectrum, similar to the Aeolian tone observed in the circular cylinder in the subcritical regime. The emergence of the dual tone is found to be responsible for the reduction of far-field noise. Continuous wavelet transform analysis reveals that the occurrence of the two competing tones in the time domain can be empirically modelled by Gaussian distributions. Additional proper orthogonal decomposition based phase averaging using time-resolved planar particle image velocimetry enables coherent vortex structure identification for the two quasi-stable shedding modes, which are responsible for the formation of the two tones. Near-wall flow and pressure fluctuation analysis further confirms that the two tones originate from stochastic shear-layer separation–reattachment switching, thereby generating two patterns of dipole sound sources through distinct vortex formation pathways.

For decades, it has been established that there are two distinct types of instability waves leading to rotating stall in compressors, known as modes and spikes. Modal-type stall inception can be explained by conventional stability theory; however, spike-type instabilities are inherently nonlinear, whose exploration requires a different theoretical approach. For this problem, a two-dimensional point vortex instability model is developed in this paper. This simple model represents a cascade of blades by a row of bound vortices and large-scale shed vortices by point vortices. It assumes that lift on an overloaded blade abruptly drops as local incidence exceeds a critical value, analogous to leading edge stall of an isolated aerofoil, such that local cascade characteristic can be expressed as a discontinuous function. The nonlinearity thus introduced precludes the possibility of modal-type inception. As the results show, a localised stall cell will be formed in the cascade once a local perturbation triggers a discontinuous drop in blade loading, which is bounded by the stall and starting vortices shed respectively from the stalling and unstalling blades. Accordingly, a spike appears in the calculated velocity or pressure trace, directly growing into rotating stall. With this model, the experimentally observed features of spike stall are qualitatively reproduced. Moreover, the temporal variation of the stall cell size is predicted for the first time, showing qualitative agreement with existing experiments. Finally, a new prediction is made that the spike amplitude increases approximately linearly with time, in contrast to the exponential growth of linear modes.

Three-dimensional laminar flow over an inclined spinning disk is investigated at a Reynolds number of ${\textit{Re}} = 500$ and an angle of attack of $\alpha = 25^\circ$, for tip-speed ratios up to 3. Numerical simulations are performed to investigate the effect of spin on the aerodynamics and characterise the instabilities that occur. Increasing tip-speed ratio significantly increases both lift and drag monotonically. Several distinct wake regimes are observed, including vortex shedding in the non-spinning case, vortex-shedding suppression at moderate tip-speed ratios and a distinct corkscrew-like short-wavelength instability in the advancing tip vortex at higher tip-speed ratios. Vorticity generated by the spinning disk strengthens the advancing tip vortex, inducing a spanwise stretching in the trailing-edge vortex sheet. This helps to dissipate the vorticity, which in turn prevents roll up and suppresses vortex shedding. The short-wavelength instability shows qualitative and quantitative matches to the $(-2,0,1)$ principal mode of the elliptic instabilities seen in pairs of counter-rotating Batchelor vortices. The addition of vorticity from the disk rotation significantly alters the circulation and axial velocity in the tip vortices, giving rise to elliptic instability despite its absence in the non-spinning case. In select cases, lock-in between the frequency of the elliptic instability and twice the spin frequency is observed, indicating that disk rotation acts as an additional forcing for the elliptic instability. Additional simulations at different Reynolds numbers and angle of attacks are considered to examine the robustness of observed phenomena across different parameter combinations.

In this experimental study, we investigate, for the first time, the structure and evolution of the near wake of a circular cylinder in a flowing soap film at the onset of vortex shedding. The study primarily focuses on the changes occurring within the recirculation bubble, along with the evolution of vortex shedding. A significantly large recirculation bubble forms behind the cylinder in the soap film environment, characterized by small-scale vortices along its edges, an observation that starkly contrasts with its three-dimensional counterparts. These small-scale vortices driven by the Kelvin–Helmholtz instability, further induce a transverse deflection of the recirculation bubble, leading to an intermittent generation of the wake vortices. The instantaneous velocity field in the wake is examined, highlighting the clear evidence of intermittency in vortex formation. The frequency and wavelength of the chain of small-scale vortices on the recirculation bubble is evaluated, and a functional relationship with the flow Reynolds number is determined. We believe this observation to be novel, potentially revealing a new pathway for understanding the two-dimensional transition in bluff-body wakes.

This paper investigates the flow past a flexible splitter plate attached to the rear of a fixed circular cylinder at low Reynolds number 150. A systematic exploration of the plate length ($L/D$), flexibility coefficient ($S^{*}$) and mass ratio ($m^{*}$) reveals new laws and phenomena. The large-amplitude vibration of the structure is attributed to a resonance phenomenon induced by fluid–structure interaction. The modal decomposition indicates that resonance arises from the coupling between the first and second structural modes, where the excitation of the second structural mode plays a critical role. Due to the combined effects of added mass and periodic stiffness variations, the two modes become synchronised, oscillating at the same frequency while maintaining fixed phase difference $\pi /2$. This further results in the resonant frequency being locked at half of the second natural frequency, which is approximately three times the first natural frequency. A reduction in plate length and an increase in mass ratio are both associated with a narrower resonant locking range, while a higher mass ratio also shifts this range towards lower frequencies. A symmetry-breaking bifurcation is observed for cases with $L/D\leqslant 3.5$, whereas for $L/D=4.0$, the flow remains in a steady state with a stationary splitter plate prior to the onset of resonance. For cases with a short flexible plate and a high mass ratio, the shortened resonance interval causes the plate to return to the symmetry-breaking stage after resonance, gradually approaching an equilibrium position determined by the flow field characteristics at high flexibility coefficients.

Bayesian optimisation with Gaussian process regression was performed to optimise the shape of an elastically mounted cylinder undergoing transverse flow-induced vibration. The vibration amplitude and mean power coefficient were obtained from two-dimensional numerical simulations, with Reynolds number $Re = 100$. First, shape optimisation was performed to maximise the amplitude of undamped vibrations. The optimised shape was found to be a thin crescent cylinder aligned perpendicular to the oncoming flow. The optimised shapes exhibited simultaneous vortex-induced vibration and galloping, a response which was not observed for other cylinder geometries at the same Reynolds number. Shape optimisation was also performed to maximise the power coefficient, where the power generation device was modelled as a linear damper. The power-optimised cylinders were also thin crescents, but with greater curvature compared with the amplitude-optimised cylinders. Compared with a circular cylinder, improvements in the power coefficient and efficiency of up to $523\,\%$ and $152\,\%$, respectively, were obtained.

The stability and dynamics of flows past axisymmetric bubble-shaped rigid bluff bodies have been numerically and experimentally investigated. Motivated by the shapes of bubbles rising in quiescent liquids the bluff bodies were modelled as spherical and elliptical caps. The geometries are characterised by their aspect ratio, $\chi$, defined as the ratio of the height of the bubble to the base radius, which is varied from $0.2$ to $2.0$. Linear stability analyses were carried out on axisymmetric base flow fields subject to three-dimensional perturbations. As observed in earlier studies on bluff-body wakes, the primary bifurcation is stationary, followed by an oscillatory secondary bifurcation, with the leading global mode corresponding to azimuthal wavenumber $m = 1$. The domain of stability is found to increase with aspect ratio for both of the geometries considered in the present study. The critical Reynolds number corresponding to the primary bifurcation is found to be independent of the aspect ratio when re-scaled using the extent of the recirculation region and the maximum of the reverse-flow velocity as the length and velocity scales, respectively. The wake flow features were characterised experimentally using laser-induced fluorescence and particle-image-velocimetry techniques. It is observed that the flow has a planar symmetry following the primary bifurcation, which is retained beyond the secondary bifurcation. The experimentally measured wavelengths and frequencies are in excellent agreement with the results obtained from global stability analyses. These observations were further corroborated using direct numerical simulations of the three-dimensional flow field. The critical Reynolds numbers corresponding to both primary and secondary bifurcations, and the dominant modes obtained using proper orthogonal decomposition of the experimentally measured velocity fields, are found to agree well with the global mode shapes and numerically computed flow fields.

This paper presents an experimental investigation focusing on the impact of structural damping on the flow-induced vibration (FIV) of a set of generic three-dimensional bodies, in this case, elastically mounted oblate spheroids. The objective is to identify and analyse the two primary FIV responses: vortex-induced vibration (VIV) and galloping, and how these vary with structural damping ratio. The VIV response has similarities to that observed for a sphere, reaching a maximum amplitude of approximately one major diameter. However, and not seen in the sphere case, a galloping-like response exhibits a linear amplitude growth as the reduced velocity is increased beyond the normal resonant range, akin to the transverse galloping response seen for a D-section or elliptical cross-section cylinder. By increasing the damping ratio, this aerodynamic-instability-driven response is effectively suppressed. However, increased damping also significantly reduces the VIV response, decreasing its maximum amplitude and contracting the VIV synchronisation, or lock-in, region. These results suggest that three-dimensional spheroids, as for two-dimensional cylindrical bodies such as D-section and elliptical cylinders, can encounter asymmetric aerodynamic forces that support movement-induced vibration, resulting in substantial body oscillation – beyond that expected under VIV alone. The study indicates that modifying the structural damping ratio can facilitate a transition between the VIV and galloping responses. These findings offer novel insights into the dynamics of fluid–structure interactions and have potential implications for designing structures and devices that can experience resonant flow conditions. Additionally, the energy harvesting performance of oblate spheroids has been evaluated, revealing that the afterbody significantly influences energy harvesting capabilities. Notably, an oblate spheroid can extract up to $50\,\%$ more power from the fluid flow than a sphere.

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

Fluidic levitation of different types of objects is achieved using laboratory experiments and described using simple mathematical models. Air bubbles, liquid tetrabromoethane droplets and solid spherical polytetrafluoroethylene beads were levitated in flowing water inside vertically oriented cylindrical tubes having diameters of 5, 8 and 10 mm. The centre of mass of all levitated objects was observed to undergo horizontal oscillations once a stable levitation point had been established. A simple model that considers the balance of gravitational, buoyancy and drag forces (as well as wall effects) was used to successfully predict the flow rates that are required to obtain stable levitation of objects with a range of different sizes. Horizontal motion was shown to be driven by vortex shedding of the objects in the tubes, and the dependence of the frequency of oscillation on their size was predicted.

We discuss flow-induced vibrations of an equilateral triangular prism confined to travel on a circular path when placed in the concave or convex orientations with respect to the flow. In each orientation, we consider three different initial angles for the prism. In Case 1, one side of the prism sees the flow first; in Case 2, one sharp edge sees the flow first; and in Case 3, one side of the prism is parallel to the incoming flow. We show that the response of the structure as well as the observed wake depend heavily on both the orientation and the initial angle of the prism. Case 1 exhibits vortex-induced vibration (VIV) in the concave orientation and galloping in the convex orientation. Case 2 does not oscillate in the concave orientation; however, oscillates about a mean deflection after a critical reduced velocity in the convex orientation. Case 3 exhibits small-amplitude oscillations in the concave orientation about a mean deflection, while in the convex orientation, exhibits VIV at low reduced velocities, followed by an asymmetric response with VIV features in a half-cycle and galloping features in the other half, and divergence at higher reduced velocities. These different types of responses are accompanied by a myriad of vortex patterns in the wake, from two single vortices shed in the wake in each cycle of oscillations to two vortex pairs, two sets of co-rotating vortices, and a combination of single vortices and vortex pairs depending on the prism’s orientation and its initial angle.