Time-resolved stereoscopic particle image velocimetry is employed to investigate elliptic synthetic jet vortex rings impinging onto a porous wall. The three-dimensional flow evolutions from vortex generation to impingement and subsequent transmission through the porous wall are captured by the phase-locked reconstruction method. Experiments are conducted under a constant orifice-to-wall distance (H-0/D-0 = 5) and wall porosity (phi = 50%), while four orifice aspect ratios (AR = 1, 3, 5, and 7) are selected to examine geometric effects. All elliptic vortex rings undergo axis switching before impingement, with switching intensity increasing with AR. For AR = 7, pronounced axis switching triggers vortex-ring bifurcation into two sub-vortex rings. During their interaction with the porous wall, a vortex bridge forms between the sub-rings and promotes their merging into a single vortex ring, establishing a vortex bridge-mediated merging mechanism. The porous wall significantly attenuates the transmitted vortices, with circulation and momentum flux losses increasing with AR. Enhanced axis switching and bifurcation strengthen upstream entrainment, resulting in increased radial momentum transport and up to a 35% elevation in peak streamwise mass flow rate compared with the circular case. However, higher AR accelerates downstream vortex decay and reduces momentum transport persistence due to enhanced dissipation and momentum flux loss. These findings demonstrate that aspect ratio fundamentally controls vortex topology, entrainment, and momentum transport, and reveal a trade-off between enhanced upstream mixing and reduced downstream momentum delivery, providing guidance for the design of applications involving elliptic synthetic jet vortex rings impinging on a porous wall.

Experimental investigations on the flow and drag characteristics of a laminar vortex ring impinging on a porous wall are conducted using time-resolved particle image velocimetry (PIV) and laser-induced fluorescence (LIF). Four cases with varying hole diameters ( d Subscript h Superscript asterisk d h & lowast; ${d}_{{h}}<^>*$ = 0.067-0.20) are examined at a constant porosity ( phi equals 0.75 phi = 0.75 ${\phi } = 0.75$ ). The evolution of the vortical structures is depicted by the finite-time Lyapunov exponent. To enhance the understanding of the formation of transmitted vortex rings, three-dimensional structures are constructed with LIF images in cross-sectional planes. Furthermore, the pressure fields are determined from PIV data using a physics-informed neural network that enables the calculation of the drag via the control volume method. The results reveal the unsteady behaviour of the drag with the vortex-wall interaction. In the strong-interaction stage, the drag is significantly influenced by both the momentum convection flux and the pressure terms, which are associated with the effect of d Subscript h Superscript asterisk d h & lowast; ${d}_{{h}}<^>*$ on the near-wall flow characteristics. Notably, when d Subscript h Superscript asterisk d h & lowast; ${d}_{{h}}<^>*$ = 0.20, the pressure term can make negative contributions, resulting in a local reduction in the drag. Conversely, the drag characteristics in the weak-interaction stage do not seem to depend on d Subscript h Superscript asterisk d h & lowast; ${d}_{{h}}<^>*$ . A further analysis indicates that for finite-thickness porous plates, the contributions of friction drag are significantly greater than those of form drag. Additionally, an a priori method for predicting impulse loss without quantitative measurements is proposed. Based on this method, the mean drag can be estimated, which is in good agreement with the experimental results.

Accurate in-plane displacement field estimation is a key procedure in planar 2-D particle image velocimetry (PIV). In this article, we propose an end-to-end deep learning-based model, termed recursive prediction-refinement neural network (RPR-NN), for PIV postprocessing. The proposed model estimates dense displacement fields from a single pair of PIV images using a lightweight recurrent unit that incorporates key principles of conventional optical flow solvers, including coarse-to-fine multiresolution pyramids, iterative warping-based refinement, and gradient-based optical flow constraints derived from the brightness constancy assumption. Furthermore, a spatial attention mechanism (SAM) is introduced to emphasize high-confidence features, effectively addressing the inherent sparsity of PIV images. RPR-NN is trained on the publicly available PIVDataset and achieves superior accuracy and computational running-time efficiency compared to representative PIV postprocessing methods. Quantitative assessments on synthetic datasets show that the proposed model exhibits robust generalization across diverse out-of-distribution scenarios that span a wide spectrum of particle seeding density, diameter, image noise levels, and particle displacement. Its effectiveness is further validated through challenging experimental PIV measurements across a wide range of flow regimes, including low-speed and hypersonic flows, where nonuniform particle seeding and low signal-to-noise ratios (SNRs) create substantial difficulties for conventional PIV postprocessing algorithms.

Bubble flows from underwater orifices are fundamental to gas-liquid operations, although the influence of orifice geometry on bubble dynamics and induced flows remains underexplored. Shadowgraphy and laser-induced fluorescence particle image velocimetry are employed to investigate bubbles released into a quiescent liquid from circular and elliptical orifices with aspect ratios AR = 1-4. Elliptical orifices produce smaller bubbles with higher aspect ratios and greater morphological complexity. These features result from anisotropic contact angles along the orifice edge, which induce non-uniform capillary forces and strong deformation at detachment. This mechanism drives high-amplitude zigzag trajectories, distinct from the spiral paths observed with circular orifices. A force-budget analysis attributes the enhanced lateral drift to rotation-induced forces. In the wake, circular orifices sustain coherent counter-rotating vortices, whereas elliptical orifices promote irregular shedding and multiscale structures. The induced turbulence spectra follow an approximate $-2$ scaling. Furthermore, flows from elliptical orifices exhibit a higher fractal dimension of the turbulent/non-turbulent interface and stronger entrainment, with a marked increase in the engulfment flux. These results quantify the mechanisms by which orifice geometry determines bubble dynamics and the developing flow field.

The background-oriented Schlieren technique has emerged as a promising method for visualizing density gradients and performing quantitative measurements. However, an inherent constraint of BOS is the compromise between spatial resolution and measurement sensitivity, as the BOS camera typically remains focused on the background pattern. To overcome the resolution-sensitivity constraint, a new BOS variant based on nominally directional rays is proposed in this paper. Instead of using diffuse, reflective background patterns, a spherically concave mirror etched with random dots has been used to create a dotted background that reflects rays in a directional manner. When combined with coaxial LED illumination, we demonstrate that the current setup can improve the spatial resolution of canonical BOS without compromising measurement sensitivity. Moreover, the proposed setup decouples the requirement for a small lens aperture to achieve a large depth of field, thereby significantly reducing the need for strong background illumination in high-speed BOS applications. To demonstrate the effectiveness of the proposed method in improving the BOS spatial resolution, both synthetic BOS image generations and experiments on low- and high-speed jets are conducted. The results show that the proposed BOS variant can be advantageous for measuring density-varying flows with a limited field of view.

This study focuses on the vibration behavior of a flexible membrane wing encountering an accelerating free stream, aiming to unravel its transient response. Wind-tunnel experiments are carried out to synchronously measure the time-resolved membrane deformations and surrounding flow fields. Based on the time-frequency spectrum obtained by continuous wavelet transform of the vibration signal, the time interval from the non-vibration state to the establishment of the dominant second mode state is defined as the vibration onset stage. During this stage, a chordwise first vibration mode (approximately 20 Hz) initially emerges and subsequently transitions to a second mode (approximately 40 Hz). The vibration frequency of each mode increases over time due to the increasing camber and membrane tension. The nondimensional frequencies of membrane vibration generally match the Strouhal number range reported in the literature. Time-frequency analysis reveals a coupling between the membrane vibration and the velocity fluctuations within the leading-edge shear layer. As the accelerating flow impacts, the membrane gradually approaches the shear layer, perceives the disturbances therein, and destabilizes to vibrate. Notably, the generation and transition of vibration modes stem from the coupling of Kelvin-Helmholtz instability and membrane's natural frequencies, which is due to an internal resonance within the coupled fluid-structure system. The wake retains its inherent bluff-body flow features at the beginning of the vibration onset stage, after which it becomes coupled with the membrane vibration.

Velocity field measurement techniques based on tracer particle imaging are widely employed in flow diagnostics. However, their application in complex flow environments is inevitably challenged by aero-optical aberrations. For instance, in combustion or supersonic/hypersonic environments, refractive index fields with drastic spatial variations induce severe aero optical effects, causing significant degradation of tracer particle images and compromising the accuracy of velocity measurements. To mitigate this issue, a novel technical approach for the non-blind restoration of degraded images of tracer particles via Singular Value Decomposition (SVD) of the Point Spread Function (PSF) is proposed. This method first performs SVD on PSFs obtained at multiple calibration positions within the field of view and subsequently reconstructs the full-field PSF distribution efficiently using a limited number of spatial modes and their corresponding spatial weighting coefficients. Furthermore, a Total Variation (TV) regularized Richardson-Lucy iterative deconvolution algorithm is employed to perform non-blind restoration on the degraded particle images using the reconstructed local PSFs. Through various numerical simulations, the influence of the number of SVD modes and image noise levels on the restoration performance is systematically investigated, and the restoration performance is compared with classical restoration algorithms. The results show that the proposed method works effectively in processing the sparse particle fields. It effectively recovers particle morphology blurred by aero-optical effects and substantially enhances the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) of the images, offering a new perspective for the application of tracer-based velocimetry in harsh optical environments.

Three-dimensional large eddy simulation is performed in the present study to analyze the control efficacy of synthetic jets on flow over a square cylinder in Re=180. Synthetic jets actuated by square, sinusoidal, bi-frequency, and varying duty-cycle signals are applied on the rear surface of the square cylinder in simulation. The vortex shedding pattern and streamwise vortical structures are investigated to assess the control effect of the synthetic jets. It is demonstrated that the control effectiveness can be improved with the characteristic momentum M-signal of synthetic jets. For signals with relatively low characteristic momentum, such as the square and sinusoidal signals, synthetic jets cannot fully control the wake. Dual alternating deflections of jet vortex pairs, along with 1/4f(e) frequency components, persist in the wake. Conversely, the higher-momentum signals, like bi-frequency and varying duty-cycle, generate stronger jets, eliminating deflection and synchronizing wake shedding at the excitation frequency. Tongue-like secondary streamwise vortices with a spanwise wavelength of 5.1D are observed in the wake without control. The application of synthetic jets suppresses the streamwise structures and improves the two-dimensionality in the spanwise direction. For low-momentum synthetic jets, antisymmetric K & aacute;rm & aacute;n vortices persist, but with improved spanwise uniformity, whereas high-momentum jets fully dominate the wake, suppressing shear-layer instabilities. The findings highlight the potential of optimized synthetic jet signals for effective wake flow control.

The aerodynamic validation model CAE-AVM cruise and high-lift configurations were tested in 2013 and 2018 at DNW-HST high-speed and DNW-LLF low-speed wind tunnels in the Netherlands, and a database of Mach number 0.85 civil aircraft has been created and opened for common research. In 2022 and 2023, the same high- and low-speed test models were selected for the correlation studies at the FL-62 transonic and FL-19 low-speed wind tunnels in China. Through comparative analysis of forces, pressure, and wing deformation data, good tunnel to tunnel correlation is recognized. Test data shows that the overall consistency of the aerodynamic forces and moment in European and Chinese wind tunnels is very good. The wing sectional pressure distributions and wing deformation data measured in high- and low-speed tests coincide with each other reasonably well. For some slight differences such as the shock wave position, wing deformation during the high-speed test, and the effect of different dummy setup on the low-speed support interference correction, possible reasons are analyzed with the parameters of the test setup, instrumentation and tunnel flow fields. The suggestions to the criteria for aerodynamic standard model test are provided.

The interaction between wake vortices from an upstream body and a downstream boundary layer is significant for both fundamental and practical aspects of fluid mechanics. An in-depth understanding of the underlying flow physics is crucial for numerous problems in aeronautics, architectonics, and energy related to the complex interferences between different bodies or apparatuses. The incoming wake vortices can generally be divided into streamwise, vertical, and spanwise vortices based on their axial directions relative to the coordinate system of downstream boundary layer. They interact with the downstream boundary layer in different ways. However, the spanwise wake vortex has more profound effects on the downstream boundary layer than the other two, because it simultaneously disturbs the whole span region of boundary layer. Therefore, the vortex dynamics of interaction between spanwise wake vortices and a downstream boundary layer is focused on in this review. The efforts of unveiling the flow physics related to this kind of interaction with different canonical configurations are reviewed as the geometrical complexity increases. The wake-triggered spanwise secondary vortices and the laminar-to-turbulent transition routine caused by their destabilization are highlighted in particular. The transition process characterized by the evolution of secondary vortices is distinct from that of a natural transition or a bypass transition induced by freestream turbulence and is commonly encountered in flows around complex geometries. Finally, areas that deserve more attention in future work are outlined and discussed.

This study investigates how the nozzle-to-wall spacing (H/D) affects the heat transfer of an impinging sweeping jet, using time-resolved particle image velocimetry and lifetime-based thermographic phosphor thermometry. Experiments are conducted at a constant Reynolds number (Re swj = 2135), volume flow rate (20 L/min), and initial wall temperature (Tw0 = 393 K), with the H/D is set to 1.5, 3.0, and 5.0 for comparison. For all H/D cases, the sweeping jets exhibit nearly identical jet spreading angles and sweeping frequencies. The flow fields also show self-similarity, with the radial profiles of both the mean velocity and root-mean-square velocity fluctuations well described by a bimodal fitting function using the same parameters. The influence of H/D is primarily observed in the near-wall flow characteristics and the resulting heat transfer performance. As H/D decreases, key near-wall flow parameters, including the radial velocity, root-mean-square radial velocity, vorticity, and Reynolds shear stress, are systematically increased. Moreover, a decrease in H/D leads to the formation of a more intense primary vortex closer to the centerline and promotes wall-jet development. This process enhances both the turbulent kinetic energy near the centerline and the periodic kinetic energy in the far field. These flow modifications explain the observed heat transfer enhancement with decreasing H/D, evidenced by both increased cooling effectiveness and a larger effective cooling area. Specifically, compared to the H/D = 5.0 case, the maximum time-averaged Nusselt number increases by 23% and 14% for H/D = 1.5 and 3.0, respectively. The correlation established between H/D-modulated flow characteristics and enhanced heat transfer provides mechanistic insight for optimizing sweeping jet impingement cooling.

Characterized by high accuracy and operational simplicity, oil-film interferometry (OFI) has served as an effective wall-shear stress (WSS) measurement technique over the past decades. It utilizes the monochromatic light interference principle to measure the temporal variation of oil-film thickness caused by WSS, and calculates time-averaged WSS based on the variation of interference fringe width. However, small-scale noise, which is caused by defects on the target surface, ambient dust, and local oil-film non-uniformity, contaminates the interference fringe patterns and directly increases the measurement uncertainty. One practical way is to apply denoising methods to improve the accuracy of identifying the centroids of fringes. In the present study, quasi-bivariate variational mode decomposition (QBVMD) is proposed as a self-adaptive denoising method to remove small-scale noise. Since no characteristic information of fringe patterns is required in the QBVMD-based denoising method, it has higher accuracy and lower uncertainty than the conventional OFI denoising methods, which need to pre-set the mask signal or the bandpass frequency, i.e., cross-correlation or spectral filtering. Thus, it facilitates the automatic identification of time-varying inhomogeneous fringes. Two sets of experiments, i.e., WSS measurement on either a canonical flat-plate turbulent boundary layer (TBL) or a TBL perturbed by micro vortex generators (MVG), were conducted to validate the applicability of this QBVMD-OFI method. The former experiment shows that the accuracy of QBVMD-OFI is equivalent to near-wall high-resolution particle image velocimetry, and is considerably higher than that of a dual hot-film sensor. As for the latter, QBVMD-OFI provides sufficient spatial resolution to resolve fine WSS structures generated by MVG.

The statistical characteristics of the translation and rotation motion of a separation shock in a hypersonic compression ramp flow are studied based on a time-resolved Schlieren image dataset. Both spectral analysis and Proper Orthogonal Decomposition (POD) indicate that the unsteady shock motion can be decoupled as low-frequency shock translation mode and high-frequency shock rotation mode. A statistical dual-Gaussian model is then proposed, in which the shock motion is described as a linear combination of two independent Gaussian processes corresponding to shock translation and shock rotation. Through a POD-mode-exclusion evaluation, it is found that this model can generally predict the statistics of full-order shock motion except for the asymmetry nature of the forth-and-back translation of the separation shock. Meanwhile, the statistics of reduced-order shock motion corresponding to pure shock rotation can be accurately predicted by the dual-Gaussian model. Additionally, a transitional shock motion characterized by strong intermittency is identified during the transition from biased shock translation to normal shock rotation.

An integrated optical system has been developed to enable simultaneous measurements of three-dimensional deformation and near-field tip vortex of flexible wings. The system combines a structured-light deformation measurement method and particle image velocimetry, operating at distinct wavelengths to avoid optical interference and achieving a fully non-intrusive measurement. Wind tunnel experiments are conducted on a simplified aircraft model equipped with one pair of rigid wings and two kinds of flexible wings at a Reynolds number of 1.1 & times; 10(5). The results show that increasing flexibility leads to larger three-dimensional deformations, with the wing tip moving upward, downstream, and spanwise inward. These deformations correlate closely with aerodynamic loading and induce corresponding vertical and spanwise displacements of the tip vortex. Despite the significant deformation as well as self-induced vibration, the radial circulation distribution of the tip vortex follows the self-similar law. Two kinds of vibration patterns, namely a bending vibration and a torsional vibration, are observed as associated with distinct patterns of vortex wandering. The bending vibration correlates with vertical wandering, and the torsional vibration enhances the spanwise wandering.

The separated and reattaching flow induced by an asymmetrically oscillating fence in a laminar boundary layer is investigated using time-resolved particle image velocimetry, with a focus on the evolution of shedding vortices, the characteristics of the turbulent/non-turbulent interface (TNTI), and the entrainment process. Fast-rising and slow-rising asymmetric oscillation modes are compared against sinusoidal oscillations, all at the resonant frequency. The results reveal that asymmetric oscillations effectively modulate vortex dynamics within individual cycles: The fast-rising oscillation enhances the core swirling strength, while the slow-rising mode generates larger-scale vortices and introduces a phase lag in their development. However, these asymmetric oscillations have negligible effects on the time-averaged statistical characteristics, such as the recirculation zone size, the vorticity thickness, and the turbulent kinetic energy distribution. The influence on the geometric properties of the TNTI, such as its height distribution, is also limited, primarily confined to the region near the fence. As for dynamic properties of the TNTI, the asymmetric oscillations accelerate the decay of the TNTI thickness, suggesting a premature breakdown of the primary shedding vortices. Despite this, the dimensionless TNTI thickness converges to a similar value after flow reattachment across all actuated cases. Regarding entrainment, the asymmetric oscillations alter the streamwise evolution of the engulfment flux near the reattachment point. Additionally, they moderately enhance the local entrainment velocity and flux associated with the nibbling mechanism within the recirculation zone, while reducing these parameters in the post-reattachment region. Nevertheless, the relative contributions of the nibbling and engulfment mechanisms to the total entrainment remain largely unchanged.

By combining the effects of synthetic jet Reynolds number (Resj), porous wall porosity (ϕ) and porous wall hole diameter (dh*), Li et al. (AIAA J 58:722–732, 2020) and Xu et al. (Phys Fluids 33:035140, 2021) presented a dimensionless similarity parameter [(Resj2d* h3)ϕ] to characterize the interaction between synthetic jet vortex rings and a porous wall. To futher incorporate the jet-exit-to-wall distance (H*) into this similarity parameter, an experimental study was conducted to inverstigate the effect of the jet-exit-to-wall distance (H* = 2, 4, 6, and 8) on the impingement of synthetic jet vortex rings onto a porous wall under three Reynolds numbers (Resj = 300, 600, and 900). By establishing the relationship between the loss of jet momentum flux and the jet-exit-to-wall distance (H*) at different Resj, a more comprehensive similarity parameter [(Resj2dh*3H*−0.64)ϕ] was derived to characterize this vortex rings-porous wall interaction. Given the substantial impact of H* on the vortex ring strength upon the impingement, an effective interaction velocity (Vj,eff = Vj/H*0.32±0.045, Vj is the characteristic velocity of the synthetic jet) was introduced, so that [(Resj2dh*3H*−0.64)ϕ] was transformed as [(Reeff2dh*)ϕ], where Reeff was the Reynolds number based on Vj,eff. This new similarity parameter effectively characterized both the losses of the momentum flux and kinetic energy transport due to impinging onto a porous wall in over 50 cases from current and previous experiments, thus verifying its validity at least in the range of [(Reeff2dh*)ϕ] ≤ 1000.

This study combines particle tracking velocimetry and thermographic phosphor thermometry to develop a new method for simultaneously measuring the flow field velocity and temperature based on the decay lifetime of phosphor particles. In this method, phosphor particles are used as tracer particles. Velocity is measured by tracking the position of the phosphor particles, and temperature is determined by obtaining the decay lifetime from multi-frame tracking of the particles’ luminescence information, achieving instantaneous and simultaneous measurements. This paper analyzes the influence of the intensity characteristics of the phosphor particles and the number of frames used in particle tracking on the temperature measurement precision. The findings indicate that using the mean intensity from a local window of the particle to calculate the temperature yields higher precision than the maximum intensity. Furthermore, increasing the number of frames used for particle tracking within a specified range enhances the precision of the temperature measurement. Calibration results over a temperature range of 20 °C–180 °C show that the uncertainty of the phosphorescence decay slope constant is 3.5

In the experimental investigation of fluid-structure interactions regarding the undulatory motion like flag flapping or fish swimming, solving the force distribution on the flexible body stands as an indispensable endeavor to gain insights into the underlying dynamic mechanisms. However, the solving process entails high-order numerical derivatives of experimental data, which poses a formidable challenge for experimental studies on fluid-structure interactions, given that the measurement noise inherent in experimental data renders the problem ill-posed. The commonly practiced regularization methods for numerical derivatives are feeble to tackle the fourth-order derivative associated with the bending force; those methods, in particular, require predetermined parameters about the unknown noise. We introduce here an empirical regularization method founded upon the kernel-term modification in the frequency domain, notably capable of determining the fourth derivative of experimental data. By leveraging the potentials of the iterative operations, our method enables the reliable estimation of an approximately optimal regularization parameter, all without reliance on any a priori knowledge about the noise characteristics. To demonstrate the reliability, robustness, and accuracy of the method, we perform rigorous numerical assessments using different data models that are infused with noise varying several orders of magnitude. Additionally, practical application of this method is achieved in the experiment on a flexible film flapping in the gusty flow, where the spatiotemporal distribution of the bending force density on the film is calculated by integrating this method with a linear reconstruction.

The dynamics of flow over an isolated surface-mounted hemisphere are investigated with tomographic particle image velocimetry (PIV). The 10 mm height hemisphere is completely submerged in the laminar boundary layer, and the height-based Reynolds number is 1530. The evolution of typical coherent structures around the hemisphere are discussed, with emphasis on the hairpin vortex (HV) and side hairpin vortex (SHV) formed periodically in the middle and both sides of the wake, respectively. Proper orthogonal decomposition (POD) analysis is conducted to explore the vortex dynamics. The shedding processes of the HV and SHV are each dominated by two different POD modes with correspondingly different characteristic frequencies, which has not been reported before in the literature. Furthermore, the coexistence of symmetric and asymmetric shedding patterns is explored for the first time in the shedding process of the HV at such a low Reynolds number. The asymmetric behaviour is controlled by the asymmetric shedding POD mode, whose dominant frequency is exactly half of the symmetric mode. In addition, SHVs on both sides of the wake are throughout formed and shed alternately, and the streamwise extensions of a horseshoe vortex also oscillate asymmetrically, which are responsible for the formation of the asymmetric shedding pattern of the HV. These findings help to fill the gaps in the related field and contribute to studies on the vortex dynamics of the flow over a hemisphere.

Characteristics of the turbulent/non-turbulent interface (TNTI) and entrainment in separated and reattaching flows induced by an oscillating fence are investigated using time-resolved particle image velocimetry. Disturbed flows are classified into subcritical, transitional, critical and supercritical cases based on the ratio of the oscillation frequency to the natural vortex shedding frequency. In the recirculation zone, distinct vortices across different cases lead to significant variations in TNTI characteristics. In the subcritical case, the TNTI evolution resembles that in the stationary fence case but with intensified height fluctuations due to the undulation of separated shear layer. For other cases, the mean TNTI height increases with the oscillation frequency, while height fluctuation diminishes. The TNTI thickness varies with nearby vortices, scaling with the Taylor microscale. After the reattachment, TNTI height distributions converge into two groups: subcritical and transitional cases exhibit larger fluctuations and positively skewed probability density functions (PDFs), while critical and supercritical cases show smaller fluctuations and basically symmetric PDFs. The TNTI thickness becomes consistent across various cases, matching the adjacent small-scale vortex size. Besides, the nibbling mechanism of entrainment aligns well with the flow development. The minimum mean entrainment velocity coincides with the strongest prograde vortex while the maximum occurs at $x\approx 1.2x_{{r}}$ (where $x$ denotes the streamwise coordinate and $x_{{r}}$ is the mean reattachment position) in all cases. Engulfment is enhanced near the reattachment location by oscillations in the transitional and critical cases, but is suppressed in the supercritical cases due to the weakness of vortex structures at higher oscillation frequencies.