Asymmetric Wake Research Articles

Wake flow behind a transversely rotating sphere confined in a pipe at low Reynolds numbers

Direct numerical simulations are performed to investigate the flow past a transversely rotating sphere confined in a pipe. Three sphere diameters of d=0.2D, 0.5D, and 0.8D (D is the pipe diameter) and sphere Reynolds numbers (based on the sphere cross-sectional mean velocity and d) of Res=250–500 are considered. The simulation results highlight the combined effects of the blockage ratio (BR=d/D) and the nondimensionalized rotation rate Ω in the range of 0.2–1.2 on the wake flow. For each BR, with increasing Res and Ω, the wake flow undergoes a transition of the flow pattern from steady symmetry and unsteady symmetry to unsteady asymmetry. For BR=0.2, the variation in flow behaviors with Ω is similar to those reported in the previous studies on a transversely rotating sphere subjected to a uniform flow. With increasing BR from 0.2 to 0.5, the unsteady asymmetric wake flow is characterized by distorted near-wake vortex rings and a series of staggered inward rolled-up vortex arcs on the double streamwise vortex threads, which results in a low-frequency modulation of the unsteady wake flow. These rolled-up vortex arcs are connected with downstream quasi-streamwise vortices and form hairpin-like vortices. Dynamic Mode Decomposition (DMD) analysis shows that the distorted near-wake vortex rings are associated with the antisymmetric DMD mode at the adjacent frequency around the symmetric primary DMD mode. With BR=0.8, there is a drastic increase in the sphere's force coefficients. A more complex wake flow behavior is found due to a strong interaction between the wake flow and the near-pipe-wall flow. At Ω=1.2, dominant asymmetric flow structures are characterized by impingement of the vortex filaments. The low-frequency modulation of these wake structures is also analyzed using the DMD analysis.

Advancements in the Understanding of Single‐Bubble Dynamics: Integrated Experimental and Simulation Studies

Because of wake instability, bubbles always ascend along an unstable path, which is not considered when simulating their movement in steel refining and continuous casting systems. Utilizing the 3D shadow image method, a quantitative characterization of the bubble trajectories is conducted to establish a bubble path oscillation model considering the zigzag lateral movement of bubbles due to asymmetric wake shedding. This model is incorporated into a rectilinear bubble motion model within the Lagrangian framework and then used to simulate the free ascent of single bubbles within the 2.15–2.55 mm range. The predicted bubble ascent velocities and trajectories agree well with the experimental. The spatial position, velocity, acceleration, forces, volume swept by bubbles, and bubble residence time are discussed. The results shown that the dominant force in the horizontal direction is the lateral force, followed by the drag and virtual mass force. Compared to the rectilinear path model, the volume swept by bubbles with initial diameters of 2.15, 2.25, 2.34, 2.45, and 2.55 mm in this model increases by 30.8%, 32.0%, 34.0%, 31.5%, and 29.6%, respectively. These findings help accurately predict the path of bubbles and also may contribute to a better understanding of bubble dynamics in bubble metallurgy and clean steel production.

Predicting the slowly converging dynamics of asymmetric vortex wakes

Predicting the slowly converging dynamics of asymmetric vortex wakes

Effects of Reynolds Number on the Wake Characteristics of a Notchback Ahmed Body

Abstract This paper investigates the effects of Reynolds number on the wake characteristics of a notchback Ahmed body with effective backlight angle, βe=17.8 deg. The Reynolds number based on the body height was varied from 5×103 to 5×104. Prior to the Reynolds number investigation, a Reynolds-averaged Navier–Stokes (RANS) model assessment was performed using nine turbulence models consisting of one- and two-equation eddy-viscosity models and second moment closure models. The standard Spalart–Allmaras model was the only model that accurately predicted the asymmetric time-averaged wake topology, as reported in previous studies, for the βe=17.8 deg notchback Ahmed body at Re=5×104. The drag coefficient decreased with increasing Reynolds number, while the lift coefficient remained constant for Re≥1×104. The wake structure exhibited three regimes: symmetric (Re≤1×104), transitionally asymmetric (1×104<Re≤3.5×104), and fully asymmetric (Re>3.5×104) states. The wake asymmetry was attributed to an imbalance in entrainment from the sides and asymmetric separation from the roof and the C-pillars of the body. The tilting and stretching terms in the vorticity transport equation were used to provide insight into the source of asymmetry in the vorticity field around the body.

A new 3D asymmetric double-Gaussian wake analytical model for horizontal-axis wind turbines

A new three-dimensional analytical model named 3DADG that is able to describe asymmetric evolution of wind turbine wake is proposed in this paper. Due to the combined effects of wind wheel rotation and wind shear effects wake attenuation shows asymmetric properties. However, existing wake analytical models fail to describe such unique properties. To solve this problem, spatial dependencies of the wake expansion rate and deficit coefficient are revealed to successfully present horizontal attenuations of the wake varying from asymmetric-double-Gaussian in the near and transition wake regions, and then to single-Gaussian in the far wake region. The wind shear effect is also considered in the model to include asymmetric vertical wake speed attenuation. This model is derived from the laws of mass and momentum conservation. It is verified through comparisons with the results of wind tunnel “blind test” and LES simulation. The model proposed is capable to show spatial evolution of wind turbine wake from a three-dimensional perspective. Sensitivities of thrust coefficient and turbulence intensity to the model are also investigated. It not only promotes development of wake analytical model but also provides a useful tool for power prediction and wake control of wind farms under wake effects.

Effect of filament length on the flow field of a rotationally oscillating cylinder with an attached filament

Experimental studies are conducted to examine the effect of filament length on the flow field and forces in the flow past a rotationally oscillating cylinder with an attached filament. The diagnostics are flow visualization through planar laser-induced fluorescence technique and characterization of the velocity and vorticity field using planar particle image velocimetry measurements. The streamwise force is estimated through control volume analysis, using an improved expression, described in Sunil et al., J. Fluid Mech. 930, A3 (2022). With an increase in the filament length, the wake structure transitions from a Kármán wake to a reverse Bénard–Kármán wake and subsequently to an asymmetric wake. This happens at a Strouhal number of StA = 0.25 and 0.6, respectively. The transition from a Kármán wake to a reverse Kármán wake precedes the drag-to-thrust transition. Thrust generation is observed to be a function of both the cylinder forcing parameters and the filament length. Shorter filaments (L/D = 0.5 and 1) produce drag, whereas longer filaments (L/D = 2, 3, and 4) produce thrust at FR≥ 2.5. Normalized values of circulation scale well with the filament length, L, and the filament tip velocity, VTE, in the case of longer filaments. The effect of filament length on vortex dynamics and thrust generation is examined through a time evolution of the instantaneous vorticity, velocity, and kinetic energy data. Maximum momentum and kinetic energy content is observed in the flow field near the instants when the vortices are shed in the wake.

Bubble–bubble interactions in two-dimensional bubble-chain flows

We experimentally investigate the bubble–bubble interactions and associated flow structures in a two-dimensional bubble chain while varying the bubble generation frequency up to 21Hz. The considered bubbles are characterized by a Bond number of around 1.0, and Archimedes and Reynolds numbers of O(102), high enough to have the shape and path instabilities. Near the nozzle (developing region), bubble trajectories and spacing between adjacent bubbles are retained (bubble-in-line arrangement), driven by the upward inertia. As the flow develops, the bubble wakes become organized and thus their interactions govern the flow. With increasing the bubbling frequency, it can be further classified into the bubble pairing, grouping, and coalescence-dominant regime. In the in-line arrangement, the trailing bubble is acceleratingly dragged to the wake behind the leading bubble, which are rearranged in tandem by the asymmetric wake. With increasing the bubbling frequency, the bubbles form a group, rapidly diffusing the jet-like liquid flow horizontally. As the vertical inertia (inviscid mechanism) dominates, the coalescence occurs frequently and the horizontal spreading of the liquid flow is suppressed substantially. By analyzing the time-averaged and fluctuating liquid velocity fields, we explain the bubble–bubble interactions in relation to the consequent modulation of the liquid-phase flow.

Features and mechanisms of asymmetric wake evolution downstream of two parallel circular cylinders

Uniform flow past side-by-side circular cylinders is a classical fluid dynamic model that triggers rich phenomena, from which asymmetric wakes usually emerge. Such asymmetry arising from a completely symmetric geometric setting is of theoretical interest when exploring the system bifurcations. Using direct numerical simulation, a detailed parametric map of the wakes behind two side-by-side circular cylinders is presented with several asymmetric wake patterns. These include asymmetric anti-phase (AAP), typical and special deflected (DF), and in-phase (IP) flows, for which AAP and special DF flows are discovered for the first time. Additionally, the IP flow is simulated by both two- and three-dimensional grids to explore the effect brought by three-dimensional vortical structures. The evolution of these asymmetric wakes is analyzed in different phases, with the aid of the wavelet transform, Hilbert–Huang transform, and dynamic mode decomposition, to reveal their temporal variations of developing features. Interestingly, although revealing with distinct fully developed flow fields, there are several common dynamics identified among these wake patterns: AP and IP vortex shedding, wake transition, and gap flow oscillation. The vicissitudes of dynamic flow evolution allow us to further differentiate several wake patterns and ultimately contribute to a deeper understanding of asymmetric flows.

Effect of upstream flow characteristics on the wake topology of a square-back truck

The influence of upstream flow characteristics on the bi-stable flow structure in the wake region of a simplified square-back heavy vehicle model at a Reynolds number of 2.7 × 104 was investigated by using the improved delayed detached eddy simulation method. The asymmetric wake structure of this model and its corresponding aerodynamic response were examined, aiming to identify the effect mechanism of three inlet profiles on the asymmetric wake structure of the named ground transportation system (GTS) model in simulations. The accuracy of the numerical method used in this study was validated by comparison with wake structure data, including the flow states, vortex core's location, and aerodynamic drag obtained from previous large eddy simulations and water channel experiments. The numerical results show that different turbulent inlet velocity profiles lead to different wake topologies. When the turbulent velocity profile with a turbulence intensity of 15% generated by TurbSim, a stochastic inflow turbulence tool for generating turbulent velocity inlet on an atmospheric boundary layer profile, is used, the expected bi-stable flow topology is still observed, but it is not shown in the case by means of the turbulence generator incorporated into ANSYS Fluent. Those turbulent inlet velocity profiles contribute to the increase in GTS model's aerodynamic drag forces. Compared to the uniform velocity profile, the TurbSim velocity profile can achieve a drag increase in 7.23%. In addition, this turbulent profile intensifies the flow fluctuations in the wake region and enhances the transient response frequency of the wake region. Thus, when assessing the vehicle aerodynamic performance in open air, especially under crosswinds, the real turbulence velocity profile, e.g., the profile generated by TurbSim in the current study, is recommended to be used for a more accurate prediction in numerical simulations.

Three-dimensional wake transitions of steady flow past two side-by-side cylinders

Three-dimensional (3-D) wake transitions of a steady flow past two side-by-side circular cylinders are investigated through Floquet analysis and direct numerical simulations (DNS) over the gap-to-diameter ratio $g^*$ up to 3.5 and Reynolds number ${\textit {Re}}$ up to 400. When the flows behind two cylinders form in-phase and anti-phase wakes at large $g^*$ , the wake transition is similar to the isolated cylinder counterpart, with the critical ${\textit {Re}}$ for the onset of 3-D transition ( ${\textit {Re}}_{cr-1}$ ) happens at around 180. At small $g^*$ , 3-D transition becomes interestingly complex due to the distinct characteristics formed in base flows. The ${\textit {Re}}_{cr-1}$ suddenly drops to around 60–100 and forms distinct variation trends with $g^*$ . Precisely, the ${\textit {Re}}_{cr-1}$ of the single symmetric wake (SS, $g^*\lessapprox 0.25$ ) is more than half of the isolated cylinder counterpart due to the large length scale of the SS wake. Only mode A is detected in SS. In the asymmetric single wake (ASS, $g^* \approx 0.25\unicode{x2013}0.6$ ) and flip-flop wake (FF, $g^* \approx 0.6\unicode{x2013}1.8$ ), the 3-D transition develops at ${\textit {Re}} \approx 103\unicode{x2013}60$ and 75–60, respectively. The decrease in ${\textit {Re}}_{cr-1}$ with increasing $g^*$ is because of the increased level of wake asymmetry in ASS and irregular vortex shedding in FF. Floquet analysis predicts two new unstable modes, namely mode A $'$ and subharmonic mode C $'$ , of ASS. Both modes are transient features in 3-D DNS and the flow eventually saturates into a new 3-D mode, mode ASS. The gap flow of mode ASS is distinctly characterised by its time-independent spanwise waviness structure that is deflected towards different transverse directions with a long wavelength of about $14$ cylinder diameters. The 3-D mode of the FF is irregular both temporally and spatially. Variations of ${\textit {Re}}_{cr-1}$ with $g^*$ , the characteristics and the physical mechanisms of each 3-D mode are discussed in this study.

Propulsive performance and vortex dynamics of jellyfish-like propulsion with burst-and-coast strategy

The propulsive performance and vortex dynamics of a two-dimensional model for the jellyfish-like propulsion with burst-and-coast strategy are investigated using a penalty-immersed boundary method. The simplified model comprises a pair of pitching flexible plates with their leading edges connected. The effects of two key parameters are considered, i.e., the duty cycle (DC, the ratio of the closing phase to the whole period) and the bending stiffness (K). Three different wake patterns, i.e., periodic symmetric, periodic asymmetric, and chaotic wakes, are identified in the DC–K plane. Numerical results indicate that a significant fast-close-slow-open motion is more likely to achieve higher speed, efficiency, and stability than a slow-close-fast-open motion, and proper higher bending stiffness is conducive to improving efficiency. A force decomposition based on the weighted integral of the second invariant of the velocity gradient tensor is performed to gain physics insight into the self-propulsive mechanism. It is found that the repulsive force induced by the strain-rate field between the body and the previous vortex pair is the main driving force of the jellyfish-like motion and that capturing the previous vortex pair during the closing phase can significantly enhance the strain rate as well as the thrust. This clarifies why the jellyfish can achieve thrust by pushing back vortex pairs. This study provides inspiration for the design and control of flexible jet propulsion devices.

Effect of morphology and an upstream tall building on the mean turbulence statistics of a street canyon flow

The effects on turbulent street canyon flow of the morphological model and the existence of an upstream tall building are investigated in a wind tunnel, using Stereoscopic Particle Image Velocimetry (S-PIV) measurements on two orthogonal vertical planes. The cathedral in the “Rue de Strasbourg, (Nantes, France)” morphological model is regarded as a local tall building and is tested and then replaced by generic, square planform buildings of 4 different heights. The cathedral induces an asymmetrical wake while no obvious different influence on the street canyon flow can be identified, in comparison with a generic building of the same height. A strong along-canyon flow occurs which may be due to the intersections, while the along-canyon ventilation decreases with increasing building height. The higher the building, the stronger its sheltering effect, leading to a reduction of the vertical ventilation and mass transport across the canyon opening, at least in the canyon portion directly downstream of the building.

A Vorticity‐Divergence View of Internal Wave Generation by a Fast‐Moving Tropical Cyclone: Insights From Super Typhoon Mangkhut

AbstractTropical cyclones (TCs) are powered by heat fluxes across the air‐sea interface, which are in turn influenced by subsurface physical processes that can modulate storm intensity. Here, we use data from 6 profiling floats to recreate 3D fields of temperature (T), salinity (S), and velocity around the fast‐moving Super Typhoon Mangkhut (western North Pacific, September 2018). Observational estimates of vorticity (ζ) and divergence (Γ) agree with output from a 3D coupled model, while their relation to vertical velocities is explained by a linear theoretical statement of inertial pumping. Under this framework, inertial pumping is described as a linear coupling between ζ and Γ, whose oscillations in quadrature cause periodic displacements in the ocean thermocline and generate near‐inertial waves (NIWs). Vertical profiles of T and S show gradual mixing of the upper ocean with diffusivities as high as κ ∼ 10−1 m2 s−1, which caused an asymmetric cold wake of sea surface temperature (SST). We estimate that ∼10% of the energy used by mixing was used to mix rainfall, therefore inhibiting SST cooling. Lastly, watermass transformation analyses suggest that κ > 3 × 10−3 m2 s−1 above ∼110 m depth and up to 600 km behind the TC. These analyses provide an observational summary of the ocean response to fast‐moving TCs, demonstrate some advantages of ζ and Γ for the study of internal wave fields, and provide conceptual clarity on the mechanisms that lead to NIW generation by winds.

Experimental Study of Turbulent Wake Flow Around Trapezoidal Cylinders With Varying Streamwise Aspect Ratios

AbstractThe effects of streamwise aspect ratio (AR) on the asymmetric wake flow over and behind right-angled trapezoidal cylinders with AR (= upper cylinder length to height ratio) = 1, 2, 3, 4, and 5 were investigated using particle image velocimetry. The Reynolds number based on the freestream velocity and cylinder height was 14700. The flow characteristics are examined in terms of the mean velocity flow, Reynolds stresses, probability density function (PDF), and two-point correlations. The results show that the primary vortex in the AR1 and AR2 trapezoidal cases extends into the wake region but is confined to the surface of the longer cases and two asymmetrical wake vortexes are only observed in the longer cases. Dual peaks of elevated streamwise Reynolds stresses are observed in the wake region, regardless of the aspect ratios. The magnitudes of the Reynolds stresses and turbulent kinetic energy are higher in the shorter cases (AR1, AR2, and AR3 cases) compared to the longer cases. The PDF distributions show a bimodal asymmetrical shape in the shorter cases but a nearly Gaussian distribution in the AR5 case. Two-point autocorrelations of the streamwise and vertical velocity fluctuations revealed that the spatial coherency of the turbulent structures is highly sensitive to the streamwise aspect ratio and reference locations. Systematic comparison between the present asymmetric results and symmetric wakes generated by rectangular cylinders with similar aspect ratios and Reynolds number shows significant differences between the asymmetric and symmetric wakes, especially at smaller aspect ratios.

Vertical Axis Wind Turbine Layout Optimization

Vertical Axis Wind Turbines (VAWTs) are not mature enough yet for offshore wind farms, but they offer benefits compared to conventional Horizontal Axis Wind Turbines (HAWTs). Higher power densities, reduced wakes, lower center of mass, and different power and thrust curves make VAWTs an interesting option to complement existing wind farms. The optimization of wind farm layouts—finding the optimal positions of wind turbines in a park—has proven crucial to extract more energy from conventional wind farms. In this study, we build an optimizer for VAWTs that can consider arbitrarily shaped layouts as well as obstacles in the area. We adapt a recent model for the wakes of VAWTs considering a Troposkien design. We can then model and optimize a large VAWT park in a real wind scenario and assess for the first time its performance operating Troposkien VAWTs. In addition, we present a novel model for wind farm optimization that considers the clockwise and counterclockwise rotation of turbines. This optimization exploits the asymmetric wakes of VAWTs, thus increasing the total energy production. We benchmark our optimization on realistic instances and compare VAWTs and HAWTs wind farm layouts, showing that VAWTs can achieve higher density and power production than HAWTs in the same area. Finally, the wake loss reduction is compared to the literature.

Asymmetric wakes in flows past circular cylinders confined in channels

In this paper, we investigate the flow past a circular cylinder confined in a channel at a blockage ratio of $\beta =0.7$ (the ratio of the cylinder diameter and the channel height) for Reynolds numbers between ${\textit {Re}}=300$ and $3900$ using direct numerical simulation (DNS). We show for varying Reynolds numbers a wide range of wake dynamics occur as the spanwise domain length is changed. At a lower Reynolds number of ${\textit {Re}}=300$ , a reverse von Kármán wake alongside either a top- or bottom-biased asymmetry was observed at different spanwise locations. The asymmetry was structurally similar the two-dimensional asymmetry studied by prior investigators, and was found to be a result of the confinement effect. Further, wake-jumping between the two intermittent states was present. For larger Reynolds numbers, ${\textit {Re}}=1000$ and $3900$ , these asymmetric structures were found to become dominant. We also examine the dependence of the asymmetries on the spanwise domain. For small spanwise domains the asymmetries were uniformly orientated across the span. In contrast, for sufficiently large spanwise domains, the asymmetry flips its orientation at different spanwise locations. Comparisons of flow statistics demonstrate good agreement between the different spanwise domains, which suggests the same mechanism maintains the asymmetry in both cases. Further analysis at ${\textit {Re}}=1000$ found the number of times the wake flips is dependent on the initial conditions, with a wake that flips zero (purely asymmetric), two and four times being observed. These structures were also determined to remain stable over time scales of $1000D/U$ .

The role of transverse inclination on the flow phenomenology around cantilevered prisms and the tripole wake mode

This work conducted wind tunnel experiments and high-fidelity numerical simulations to study the flow phenomenology around and aerodynamic characteristics of a transversely inclined cantilever prism—a highly probable but unattended configuration when inclined civil structures are subjected to changing angle of attack. The velocity field, stream and spanwise vorticity, Q-criterion vortex structures, aerodynamic force and spectra, surface pressures, and shear layer morphology have been comprehensively analyzed. Results showed significant deviations from the vertical prism, deeming many classical observations on the prism wake untransferable to the inclined cases. The underlying flow phenomenology was subsequently clarified. Transverse inclination induces a fundamentally different, asymmetric wake morphology, especially near the fix- and free-end, suppressing the horseshoe vortices and intensifying near-wake turbulence. The prism base also experiences a remarkable intensification of wind load and vortical dynamics. The suppression of vortical activities on the near-wind side of the fix-end also gives rise to a new wake morphology – the tripole mode – unique to transverse inclination. Moreover, transversely inclined prisms experience different crosswind loads when angle of attack reverse in sign, which is attributed to changes in shear layer curvature. This work’s conclusions partially fill the gap in the fluid mechanics of inclined prisms and, more importantly, highlight the extra cautions needed for engineering applications involving inclined structures.

Synergistic analysis of wake effect of two cylinders on energy harvesting characteristics of piezoelectric flag

In this study, the effect of asymmetric wake flow regime of two side-by-side cylindrical bluff bodies on power output is experimentally examined by using a piezoelectric flag. Different synchronization modes of the flag with wake flow are observed. It is demonstrated that the streamwise gap between the flag and cylinders (Gx), and the center-to-center gap between cylinders have a significant impact on the flag's dynamical behavior that results in a fluctuation in the power output of the piezoelectric flag. The levels of output power are analyzed by varying the Gx and the cross-stream or lateral gap (N/d) between the two cylinders. N/d values from 1.0 to 2.0 for different values of Gx (2.0 ≤ Gx ≤ 4.0) are experimentally tested. The comparison of the flapping response at each point is made to ascertain the impact of the harvester's dynamic behavior on the output energy. The power generated at each point is recorded for all cases and a comparative analysis is made to find the optimal configuration. Limited research is conducted in the past to enhance the energy output by using the bluff body with the improved wake dynamics. Hence, two cylinders are employed in a uniform flow and crosswise gap between cylinders is varied to change the characteristics of the wake region. The cylinder arrangement with N/d = 1.0, shows continuous oscillations and higher output power persisting for 2.0 ≤ Gx ≤ 4.0. The monotonic rise in power output is observed till Gx = 4.0. The stated configurations with N/d = 1.0 gives a significant advantage over a single-cylinder-based energy harvester as a kinetic source of fluid energy harvester from the flowing fluid. The output power became almost doubled with an increase of 95% approximately using side-by-side arrangement.

Applicability of Dynamic Inflow Models of HAWT in Yawed Flow Conditions

Horizontal axis wind turbines (HAWTs) experience yaw misalignments due to the physical limitations of yaw controllers and various novel active yaw controls. Moreover, the motion of floating offshore wind turbines (FOWTs) accelerates yaw misalignment. The blade element momentum (BEM) method is widely used due to its computational efficiency for the design of HAWTs. Momentum theory, the basis of BEM, assumes steady flow and uniform induction field at the disc. Those assumptions are relaxed by engineering models to capture yaw and unsteady effects. Current yaw engineering models, however, are inaccurate since they do not capture the asymmetric wake expansion effect. Dynamic inflow models have been developed for non-yawed flow. Furthermore, the AVATAR project shows that BEM using fully coupled engineering models, the current yaw, dynamic inflow and various engineering models, suffers from significant deficiencies. This purpose of this paper, therefore, is to investigate dynamic effects for yawed flow, and determine if current dynamic inflow models are applicable in yawed conditions. The Glauert’s modified momentum theory is applied to dynamic inflow models to couple the two models. Among all coupled models, Øye, Yu PWVM and Yu FWVM DIM can capture asymmetric trends. However, the results show the significant deficiencies in phase delay on the actuator disc.

Asymmetric wake, origin, generation, and suppression behind asymmetrically pitching hydrofoil

The wakes behind a symmetrically and a quasi-symmetrically pitching hydrofoil are numerically studied. To understand the generation mechanism of the asymmetric wake behind a symmetrically pitching hydrofoil, we shed light on the timing of vortex shedding and convection velocity of vortices in the wake. The centers of the vortices in the wake are tracked using a method based on the critical point theory. The tracks of the vortex centers reveal crucial insights into the dependence of the vortex convection velocity on pitching frequency and pitching amplitude. The vortex strength and the spatial separation between the vortices embody the wake deflection. We find the inherent inability of the shear-layer rolling up at par with the pitching motion results in an uneven temporal separation (Δtʹ) between two consecutive vortices, which dictates the spatial separation between the vortices. The uneven temporal separation facilitates formation of vortex dipoles, which gives rise to the asymmetric wake formation. To substantiate the hypothesis of the uneven temporal generation of vortices, we used quasi-symmetric pitching of the hydrofoil, which can even the timing of vortex shedding and can metamorphose the asymmetric wake into a symmetric wake. On the contrary, relaxing the shear-layer roll-up can transmute a symmetric wake to an asymmetric wake. The detailed analysis of symmetrically pitching hydrofoil, quasi-symmetrically pitching hydrofoil, flexible hydrofoil, and asymmetrically pitching hydrofoil reveals that Δtʹ = 0.5, Δtʹ < 0.5 and Δtʹ > 0.5 correspond to a symmetric wake, an upward deflected wake and a downward deflected wake, respectively.