The flow-induced oscillations of a clamped flexible ring in a uniform flow were explored using the penalty immersed boundary method. Both inverted and conventional ring configurations were examined, with systematic analysis focused on the effects of bending rigidity and eccentricity. Four distinct oscillation modes were identified across parameter variations: flapping (F), deflected oscillation (DO), transverse oscillation (TO) and equilibrium (E) modes. Each mode exhibited a 2S wake pattern. The inverted ring sustained the DO mode under low bending rigidity with a deflected shape, transitioning to the TO mode at higher bending rigidity. In the TO mode, a lock-in phenomenon emerged, enabling the inverted ring to achieve a high power coefficient due to a simultaneous rise in both oscillation amplitude and frequency. By contrast, the conventional ring exhibited the F mode at low bending rigidity and transitioned to the E mode as rigidity increased, although its power coefficient remained lower because of reduced critical bending rigidity. For the inverted ring, low eccentricity enhanced oscillation intensity but limited the operational range of the TO mode. In contrast, for the conventional ring, reducing eccentricity led to an increase in oscillation amplitude. Among the investigated configurations, the inverted-clamped ring achieved the highest energy-harvesting efficiency, surpassing those of the conventional clamped ring and a buckled filament.

The flow-induced oscillation of a transversely clamped buckled flexible filament in a uniform flow was explored using the penalty immersed boundary method. Both inverted and conventional configurations were analysed. The effects of bending rigidity, filament length and Reynolds number were examined. As these parameters were varied, four distinct modes were identified: conventional transverse oscillation mode, deflected oscillation mode, inverted transverse oscillation mode and structurally steady mode. The filament exhibited a 2S wake pattern under the conventional transverse oscillation mode and the small-amplitude inverted transverse oscillation mode, a P wake pattern under the deflected oscillation mode and a 2S + 2P wake pattern for the large-amplitude inverted transverse oscillation mode. Irrespective of their initial conditions, all of the filaments converged to the conventional transverse oscillation mode under low bending rigidity. Multistability was observed in the transversely clamped buckled flexible filament under moderate bending rigidity. The deflection in the oscillation mode increased with increasing filament length. The inverted buckled filament was sensitive to the Reynolds number, unlike the conventional buckled filament. The transverse oscillation mode demonstrated superior energy-harvesting performance.

The flow-induced oscillation of an S-shaped buckled flexible filament was explored using the penalty immersed boundary method. As the length and bending rigidity of the filament were varied, three distinct modes emerged: the equilibrium mode, streamwise oscillation (SO) mode and transverse oscillation (TO) mode. A transition region between the SO and TO modes was identified. Notably, the filament exhibited a 3P wake pattern under SO and a 2S wake pattern under TO. The former was induced by fluid–elastic instability, while the latter was attributed to vortex-induced oscillation. The interaction between the filament's motion and vortex shedding was examined for both modes. To elucidate the disparity between the TO of the S-shaped buckled filament and snap-through oscillation (STO), a ball-on-a-hill analogy was introduced. The performance of energy harvesting was evaluated using metrics including the elastic energy and power coefficient. The TO mode was found to show significantly higher energy harvesting performance than the SO and STO modes. The majority of the strain energy was concentrated at the upper and lower midpoints of the filament.

The present study offers a twofold contribution on counter-gradient transport (CGT) of turbulent scalar flux. First, by examining turbulent scalar mixing through synchronized particle image velocimetry and planar laser-induced fluorescence on an inclined jet in cross-flow, we clarify the previously unexplained phenomenon of CGT, revealing key flow structures, their spatial distribution and modelling implications. Statistical analysis identifies two distinct CGT regions: local cross-gradient transport in the windward shear layer and non-local effects near the wall after injection. These behaviours are driven by specific flow structures, namely Kelvin–Helmholtz vortices (local) and wake vortices (non-local), suggesting that scalar flux can be decomposed into a gradient-type term for gradient diffusion and a term for large-eddy stirring. Second, we propose a new approach for reconstruction of turbulent mean flow and scalar fields using continuous adjoint data assimilation (DA). By rectifying model-form errors through anisotropic correction under observational constraints, our DA model minimizes discrepancies between experimental measurements and numerical predictions. As expected, the introduced forcing term effectively identifies regions where traditional models fall short, particularly in the jet centreline and near-wall regions, thereby enhancing the accuracy of the mean scalar field. These enhancements occur not only within the observation region but also in unseen regions, underscoring present DA approach's reliability and practicality for reproducing mean flow behaviours from limited data. These findings lay a solid foundation for adjoint-based model-consistent data-driven methods, offering promising potential for accurately predicting complex flow scenarios like film cooling.

Three-dimensional effects of sidewalls on the low-frequency unsteadiness of the shock-wave/boundary-layer interaction (SBLI) are of academic and practical importance but not yet well understood. Considerable attention has been paid to the viscous effect of sidewalls, whereas the potential inviscid confinement effect of sidewalls has received little attention. The present work provides experimental evidence of multiscale spanwise travelling waves crossing the separation front under the confinement of sidewalls. Global pressure measurements were made for a sidewall-confined 24$^\circ$ compression ramp interaction in Mach-2.83 flow using fast-responding pressure-sensitive paint. The unsteady pressure in a statistically two-dimensional intermittent region suggests that in addition to the canonical streamwise oscillation, the separation front exhibits significant low-frequency, multiscale spanwise distortion. Modal analysis further reveals that multiscale spanwise unsteadiness has higher intensity and frequency than the streamwise oscillation. Such strong spanwise unsteadiness calls attention to the low-frequency unsteadiness in previous sidewall-confined SBLI experiments and encourages further study on the mechanism of the confinement effect.

This study presents the interplay of flow and acoustics within tandem deep cavities, focusing on the resonance mechanism occurring between turbulent shear layers and acoustic eigenmodes. The arrangement inside the tandem deep cavities includes both close and remote configurations. A combined fully coupled and decoupled aeroacoustic simulation strategy was devised. Employing an advanced high-order spectral/hp element method in conjunction with implicit large eddy simulation, the nonlinear compressible Navier–Stokes equations were solved to acquire internal flow–acoustic resonant field. In parallel, the linearized Navier–Stokes equations were tackled to determine coherent shear layer perturbations with external acoustic forcing. Based on acoustic measurements, the mainstream Reynolds number approaches approximately $R{e_{in}} = {O}({10^5})$, where we identified the presence of frequency lock-in and a resonance range. Aeroacoustic noise sources were examined by implementing spectral proper orthogonal decomposition to decompose the pressure fields into hydrodynamic and acoustic components. As feedback intensified, the flow characteristics by the acoustic forcing effect and the flow-interactive effect were categorized according to the development of concurrent turbulent shear layers. Subsequently, the alternating and synchronous behaviours of concurrent shear layers resonated with the out-of-phase and in-phase acoustic eigenmodes were identified, and the corresponding large-scale counter-rotating vortex pairs and co-rotating vortex structures at the cavity entrances were extracted. The acoustic power generated by the Coriolis force was calculated using Howe's vortex-sound analogy, and the aeroacoustic energy transfer mechanism between large-scale shear layer vortices with acoustic eigenmodes was further explored. Finally, a linear response of coherent perturbations of the concurrent shear layers by external acoustic forcing was established. The amplification of flow in the streamwise direction toward the main duct led to the formation of coherent vortex structures, accompanied by separation bubbles into the main duct.

The super-temporal-resolution (STR) reconstruction of turbulent flows is an important data augmentation application for increasing the data reach in measurement techniques and understanding turbulence dynamics. This paper proposes a data assimilation (DA) strategy based on weak-constraint four-dimensional variation to conduct an STR reconstruction in a turbulent jet beyond the Nyquist limit from given low-sampling-rate observations. Highly resolved large-eddy simulation (LES) data are used to produce synthetic measurements, which are used as observations and for validation. A segregated assimilation procedure is realised to assimilate the initial condition, inflow boundary condition and model error separately. Different types of observational data are tested. The first type is down-sampled LES data containing many small-scale turbulence structures with or without synthetic noise. The DA results show that the temporal variation of the small-scale structures is well recovered even with noise in the observations. The spectra are resolved to a frequency approximately one order of magnitude higher than what can be captured within the Nyquist limit. The second type of observation is low-sampling-rate tomographic particle image velocimetry (tomo-PIV) data with or without the injection of small-scale structures. The modulation between the large-scale structures contained in the tomo-PIV fields and the small scales injected from the observations is improved. The resultant small scales in the STR reconstruction have the characteristics of authentic turbulence to a considerable extent. Additionally, DA yields much smaller errors in the prediction of particle positions when compared with the Wiener filter, demonstrating the great potential for Lagrangian particle tracking in measurement techniques.

The flow-induced snap-through dynamics of a buckled flexible filament was explored using the penalty immersed boundary method. The effects of the filament length, bending rigidity and Reynolds number on the mode transition were systematically examined. Three different modes were observed when the aforementioned parameters were varied: an equilibrium mode, a streamwise oscillation mode and a snap-through oscillation mode. Two mode transitions occurred when the bending rigidity was lowered and the length and Reynolds number were increased: a direct transition from the equilibrium mode to the snap-through oscillation mode and the successive appearance of the three modes. An increase in transverse fluid force induced the snap-through oscillation mode. A vortex-induced vibration and a self-excited vibration occurred in the streamwise oscillation mode and the snap-through oscillation mode, respectively. A wake pattern of 2S appeared in the streamwise oscillation mode, and a pattern of 2S + 2P appeared in the snap-through oscillation mode. A hysteresis was observed near the critical Reynolds number. The hysteresis loop increased in magnitude with increasing bending rigidity. The greater energy harvesting was achieved by the larger deflection and the higher strain energy. We found that most of the strain energy was concentrated in the last half of the filament.

The hydrodynamic mechanism of drag reduction by a flexible hairy coating was explored using the penalty immersed boundary method. A two-dimensional flexible hairy coating is constituted by multiple flexible filaments. A simulation of a cylinder without a hairy coating at a Reynolds number of 100 was also performed for comparison. The results of the simulations show good agreement with the experimental data by Niu & Hu (Phys. Fluids, vol. 23, 2011, 101701), where maximum drag reduction of 22% was attained at a particular length, bending rigidity, coating density and coating angle of the hairy coating. The hydrodynamic mechanism of drag reduction was characterized in terms of the wake pattern, shape deformation and kinetic energy of the hairy coating. The effect of a non-uniform bending rigidity of the hairy coating on drag reduction was explored. A stable streamline shape of the hairy coating was found to delay the vortex formation and stabilize the recirculation zone, resulting in decreased form drag. Active flapping of the hairy coating with enhanced vortex shedding is adverse to drag reduction. A hairy coating with a stiff base and flexible trailing edge is beneficial to maintaining a stable shape.

This paper examines the unsteady lift, drag and moment coefficients experienced by a thin airfoil in high-amplitude pitch ramp motion. Experiments have been carried out in a wind tunnel at moderate Reynolds number ( $Re\approx 1.45\times 10^{4}$ ), using a rigid flat-plate model. Forces and moments have been measured for reduced pitch rates ranging from 0.01 to 0.18, four maximum pitch angles ( $30^{\circ },45^{\circ },60^{\circ },90^{\circ }$ ) and different pivot axis locations between the leading and the trailing edge. Results confirm that for reduced pitch rates lower than 0.03, the unsteady aerodynamics is limited to a stall delay effect. For higher pitch rates, the unsteady response is dominated by a buildup of the circulation, which increases with the pitch rate and the absolute distance between the pivot axis and the $3/4$ -chord location. This circulatory effect induces an overshoot in the normal force and moment coefficients, which is slightly reduced for a flat plate with a finite aspect ratio close to 8 in comparison with the two-dimensional configuration. A new time-dependent model has been tested for both the normal force and moment coefficients. It is mainly based on the superposition of step responses, using the Wagner function and a time-varying input that accounts for the nonlinear variation of the steady aerodynamics, the pivot point location and an additional circulation which depends on the pitch rate. When compared with experiments, it gives satisfactory results for $0^{\circ }$ to $90^{\circ }$ pitch ramp motion and captures the main effect of reduced pitch rate and pivot point location.