Vortex Shedding Modes Research Articles

Numerical simulation of VIV for a circular cylinder with a downstream control rod at low Reynolds number

A numerical simulation of the vortex-induced vibration (VIV) at Reynolds number of 500 is carried out for a circular cylinder with a downstream rigidly connected control rod. The mass ratio (m*) and damping ratio (ξ) are fixed as 10 and 5×10−4. The fluid dynamics is obtained by solving arbitrary Lagrangian–Eulerian (ALE) Navier–Stokes equations, and the structure dynamics is solved using Newmark-β method. The grid convergence is tested using five different grids to select the proper mesh. The model and computational method are validated by comparing with the previous research, and a good agreement is reached. The VIV of the cylinder system at eight different gap ratios (G∕D=0.01∼2) are simulated. The responses of the cylinder system are discussed following the classification of the flow patterns at different gap ratios. The same VIV characteristic can be observed in the same flow pattern. The sub-harmonic resonance is observed in the VIV of the cylinder system for large reduced velocity as G∕D<0.7. A simple formula is used to explain the sub-harmonic resonance. The vortex shedding mode and the frequency of the lift force on the cylinders in the lock-in regime are used to validate the formula. The smaller the gap ratio is, the more lock-in regimes can be excited, and the higher-order sub-harmonic resonance can be observed. The control rod has a great influence or even is decisive on the VIV of the cylinder system at small gap ratio. As the gap ratio increases, the effect of the control rod is becoming weak. Besides the natural frequency of the cylinder system, the frequency corresponding to the vortex shedding mode is observed in the lift coefficient of the cylinders.

Detached-Eddy Simulations for Active Flow Control

The present study conducted improved delayed detached-eddy simulations of actively controlled flows with a harmonic actuation on a backward-facing step and pulsed blowing on a pitching airfoil for reattachment and separation controls. Spectra analyses based on the unexcited flowfield data were carried out by using dynamic mode decomposition to identify spatial structures corresponding to the different Strouhal frequencies. The characteristic physical modes have been extracted for both cases. With better understanding of unsteady flow features, effective control practices were illustrated. For the backward-facing step case, the optimal excitation frequency was found to be identical with the step-mode frequency of the baseline flow. Such harmonic actuation enhanced the pairing process, forming the largest-scale spanwise coherent structures in the free shear layer, resulting in a 40% maximum reduction of the bubble length. For the airfoil case, with the optimum excitation frequency determined by the vortex-shedding mode of the baseline flow, a 194% increase of the lift-to-drag ratio was obtained; the pulsed blowing with the jet orifices in an antiphased manner was found to be very effective to damp the fluctuations of the lift around its mean value, though it led to a small decrease in mean lift.

Locked-on vortex shedding modes from a rotationally oscillating circular cylinder

Numerical simulations of unsteady two-dimensional flow around a rotationally oscillating circular cylinder, placed in a uniform cross flow of a constant property Newtonian fluid, are performed at a fixed Reynolds number of 200. The investigation is based on the solutions of stream function-vorticity formulation of Navier-Stokes equations on non-uniform polar grids using a higher order compact (HOC) formulation. The flow field is mainly influenced by Reynolds number, Re, maximum angular velocity of the cylinder, αm, and the frequency ratio, f/f0, which represents the ratio between the frequency of oscillation, f, and the natural vortex shedding frequency, f0. The ranges considered for these parameters are 0.5⩽αm⩽6.0 and 0.5⩽f/f0⩽3.0. The resulting vortex formation modes and lock-on phenomena behind the cylinder as well as the fluid forces acting on the cylinder are analyzed. Occurrence of new multiple lock-on regions is demonstrated in detail by the variation of f and αm. The instances of high drag reduction at high values of αm are confirmed. Comparisons with previous numerical and experimental results verify the accuracy and validity of the present study.

Effect of rounded corners on two degree of freedom naturally oscillating square cylinder

PurposeThe paper aims to study the influence of rounded corners on the flow-induced oscillation of a square cylinder that is free to oscillate in two degrees of freedom.Design/methodology/approachThe finite volume code in conjunction with the moving mesh scheme was implemented via a user-defined function to carry out the computations in two dimensions. The Reynolds number (Re) chosen for the present study is fixed at 100, and the frequency ratio, Fr = fs/fn (where fs is the vortex shedding frequency and fn is the natural frequency of cylinder) is used as a varying parameter. The computational model was validated for flow past a stationary cylinder with R/D = 0 and 0.5, and the results showed good agreement with the literature.FindingsThe aerodynamic characteristics, amplitude response, trajectories of cylinder motion and vortex shedding modes are obtained by conducting a series of simulations under different frequency ratios of the cylinder. It was found that the minimum transverse amplitude, drag force and lift force obtained for a naturally oscillating square cylinder are quite different when compared with a stationary and forced oscillating cylinder, where the maximum drag and lift forces were observed for a square cylinder and a minimum around R/D = 0.2 was observed.Originality/valueThe present work identified the significant effect of the varying frequency ratio and R/D on the VIV modes of the cylinder. It was observed that the cylinder wake exhibits the (2S) vortex shedding mode for R/D = 0 to 0.2 at all Fr, whereas the C (2S) mode appeared for R/D > 0.2 at Fr = 1.1.

Effects of oncoming flow conditions on the aerodynamic forces on a cantilevered square cylinder

The aerodynamic forces on a cantilevered square cylinder with a height-to-width ratio (H/d) of 5 in a crossflow were experimentally investigated in a closed-loop low-speed wind tunnel. The freestream oncoming flow velocity (U∞) ranged from 5 to 45 m/s, corresponding to Reynolds numbers, based on U∞ and d, of 0.68 × 105 to 6.12 × 105. Two different oncoming flow conditions were tested. In case 1, the majority of the cylinder span was in the uniform flow, except the lower 1d which was immersed in a thin turbulent boundary layer; in case 2, the tested cylinder was completely immersed in a turbulent boundary layer. In both cases, the Reynolds number had a negligible effect on the aerodynamic forces of the cylinder. The predominant vortex shedding frequency was constant along the cylinder span, regardless of the thickness and nature of the boundary layer. In case 1, the lift fluctuated periodically with a large amplitude or did not exhibit obvious periodicity, which correspond to the anti-symmetric and symmetric vortex shedding modes, respectively. Proper orthogonal decomposition (POD) analysis showed that, in case 2, anti-symmetric vortex shedding tends to occur, instead of the symmetric mode, thus resulting in a larger fluctuating lift than that observed case 1.

Passive pitching of splitters in the trailing edge of elliptic cylinders

The distinctive pitching of hinged splitters in the trailing edge of elliptic cylinders was experimentally studied at various angles of attack ($AoA$) of the cylinder, Reynolds numbers, splitter lengths, aspect ratios ($AR$) of the cylinder and freestream turbulence levels. High-resolution telemetry and hotwire anemometry were used to characterize and gain insight on the dynamics of splitters and wake flow. Results show that the motions of the splitters contain various dominating modes, e.g. $f_{p}$ and $f_{v}$, which are induced by the mean flow and wake dynamics. High background turbulence dampens the coherence of the regular vortex shedding leading to negligible $f_{v}$. For a sufficiently long splitter, namely twice the semimajor axis of the cylinder, dual vortex shedding mode exists close to the leading and trailing edges of the splitter. In general, the splitters oscillate around an equilibrium position nearly parallel to the mean direction of the flow; however, a skewed equilibrium is also possible with a strong recirculation region. This is the case with cylinders of low $AR$ and high $AoA$, where higher lift and drag occurs. Flow measurements at various transverse locations within the wake of the cylinder–splitter system indicate that the signature of the low-frequency splitter pitching is shifted in the wake in the cases with non-zero $AoA$ of the cylinder. Although the splitter pitching exhibits two dominant vortex shedding modes in various configurations, only the higher frequency is transmitted to the wake.

Vortex-induced vibrations of three staggered circular cylinders at low Reynolds numbers

Vortex-induced vibrations of three staggered circular cylinders are investigated via two-dimensional finite element computations. All the cylinders are of equal diameter (D) and are mounted on elastic supports in both streamwise (x−) and transverse (y−) directions. The two downstream cylinders are placed symmetrically on either side of the upstream body at a streamwise gap of 5D, with the vertical distance between them being 3D. Flow simulations are carried out for Reynolds numbers (Re) in the range of Re = 60-160. Reduced mass (m*) of 10 is considered and the damping is set to zero value. The present investigations show that the upstream cylinder exhibits initial and lower synchronization response modes like an isolated cylinder does at low Re. Whereas for both the downstream cylinders, the upper lock-in branch also appears. The initial and the upper modes are characterized by periodic oscillations, while the lower lock-in branch is associated with nonperiodic vibrations. The 2S mode of vortex shedding is observed in the near wake of all the cylinders for all Re, except for the upper branch corresponding to the downstream bodies. In the upper branch, both the downstream cylinders shed the primary vortices of the P+S mode. For the upstream cylinder, the phase between lift and the transverse displacement exhibits a 180° jump at certain Re in the lower branch. On the other hand, the downstream bodies undergo transverse oscillations in phase with lift in all lock-in modes, while the phase jumps by 180° as the oscillation response reaches the desynchronization regime.

Dynamic mechanism of phase differences in One degree-of-freedom vortex-induced vibration of a cylindrical structure

The purpose of this study is to provide some insights into the phase mechanism of a cylindrical vortex–induced vibration. A transient coupled fluid–structure interaction numerical model is adopted to simulate a cylindrical vortex–induced vibration. The vortex shedding around the cylinder is investigated numerically by a two-dimensional large eddy simulation approach which can catch more details of the flow field and more accuracy on computing hydrodynamic forces. The vortex shedding modes and response and hydrodynamic forces of a cylindrical vortex–induced vibration are acquired with varied frequency ratios. According to differences in the vortex shedding location, the vortex wake can be characterized by two kinds of mode, the “first mode” and the “second mode.” The mechanisms behind the phases of the first mode and the second mode vortex wakes are investigated, and it is found that the flow speed induced by a cylindrical transverse vibration and the position of a vortex release are the root causes of the phase difference between the lift coefficient and transverse displacement. The speeds caused by a cylinder vibration and a cylinder-shed vortex are the reasons that the lift amplitude of an oscillatory cylinder is different from that of a fixed cylinder.

The effect of spacing on the vortex-induced vibrations of two tandem flexible cylinders

Vortex-induced vibrations (VIVs) of two flexible cylinders arranged in tandem are studied using a two-way fluid-structure interaction (FSI) method with different spacing ratios (Sx/D) at Reynolds number Re = 500 using a two-way fluid-structure interaction (FSI) method. The main objective of this study is to investigate the effect of spacing on the hydrodynamic interactions and the VIV responses of these cylinders. The responses of the two flexible cylinders are found to be similar to the classical VIV responses at small Sx/D. Once Sx/D is large enough for the vortices to become detached from the upstream cylinder, the response of the upstream cylinder is similar to the typical VIV response whereas the downstream cylinder undergoes wake-induced vibration. The characteristics of the response of the downstream cylinder in the present study are similar to those of the first two response regimes classified by previous researchers. The third regime is not observed for the flexible downstream cylinder with both ends fixed. The two changes in the phase relation between the cross-flow displacements of the two tandem flexible cylinders are discovered to be linked with the initial-upper branch transition and the upper-lower branch transition, respectively. The correlation lengths of the two flexible cylinders decrease significantly in the transition range between the upper and lower branches. Three modes of vortex shedding (2S, P + S, and 2P) have been identified in the present study. The upper-branch 2P mode is found to be associated with large-amplitude vibration of the upstream cylinder and the P + S mode is observed to be related to large-amplitude vibration of the downstream cylinder for Sx/D = 3.5 and 5. On the other hand, the lower-branch 2P mode leads to small-amplitude vibration of the downstream cylinder in the post-lock-in range at Sx/D = 2.5. The relative phase shifts of the sectional lift coefficients on different spanwise cross sections can be attributed to the variation of the vortex shedding flow along the flexible cylinders, and these phase shifts result in poor phasing between the forces and the displacements that is related to the decrease of the correlation lengths.

Three-dimensional numerical simulation of two-degree-of-freedom VIV of a circular cylinder with varying natural frequency ratios at [formula omitted

The two-degree-of-freedom (2DOF) vortex-induced vibration (VIV) of a circular cylinder with varying in-line to cross-flow natural frequency ratios (f∗=fnx∕fny) is studied using a three-dimensional (3D) computational fluid dynamics (CFD) approach. Numerical simulation is carried out for a constant mass ratio of 2 at a fixed Reynolds number Re=500. The reduced velocity ranges from 2 to 12. Three natural frequency ratios are considered, i.e., f∗=1,1.5 and 2. The structural damping is set to zero to maximise the response of the cylinder. The main objective of this study is to investigate the effect of f∗ on the 2DOF VIV responses and the 3D characteristics of the flow. It is discovered that there is a significant increase in the vibration amplitude, and the peak amplitude shifts to a higher reduced velocity when f∗ increases from 1 to 2. A single-peak cross-flow response is observed for the identical in-line and cross-flow mass ratios when f∗=2. Dual resonance is found to exist over the range of f∗ studied. The preferable trajectories of the cylinder in the lock-in range are counterclockwise figure-eight orbits. Oblique figure-eight trajectories appear at Vr=6,7 and 8 when f∗=1. The third harmonic component which is observed in the lift fluctuation increases with f∗. The correlation decreases in the lock-in range and reaches its minimum value around the transition region between the lock-in and post-lock-in ranges. Three vortex shedding modes (2S, P + S and 2P) appear in the present simulation. A dominant P + S mode is associated with the oblique figure-eight trajectories. Variation of vortex shedding flows along the cylinder is observed leading to the poor correlation of the sectional lift forces.

The lowest Reynolds number of vortex-induced vibrations

It is well known that the occurrence of vortex-induced vibration (VIV) at a subcritical Reynolds number, which is lower than 47, is induced by fluid-structure interaction. However, for the free flow, this phenomenon disappears at a Reynolds number about 20. The current study provides an explanation to the disappearance of the VIV by capturing the evolution of the purely fluid modes at Reynolds numbers between 12 and 55. To ensure accurate mode extraction, the dynamic mode decomposition technique is utilized. Results show that the stable von Kármán vortex shedding mode exists in a subcritical flow regime but becomes less distinct as the Reynolds number decreases. When the Reynolds number is lower than 18, this mode nearly vanishes, characterizing the lower boundary of fluid-structure instability.

Extraction and Reconstruction of Individual Vortex-Shedding Mode from Bistable Flow

For the flow around a circular cylinder under the synthetic-jet control, a bistable flow has been identified, in which the wake vortex sheds with the symmetric or antisymmetric mode. However, it is difficult to gain insight into the bistable flow due to the complexity with multiple dominant frequencies. Thus, it is aimed to reveal the underlying flow physics of the bistable flow by adopting advanced data-processing techniques. To obtain more accurate dynamic information, total dynamic mode decomposition was employed to extract dynamic modes, spectrum, and mode coefficients to describe the flow dynamics. It was found that the bistable flow contains dual dominant frequencies corresponding to the antisymmetric and symmetric vortex-shedding modes. The mode for the control case approximates to the mode for the natural case, representing the antisymmetric-shedding mode. However, the spatial distributions of the mode are essentially different from those of the mode , representing the symmetric-shedding mode. The influence of the dominant modes and of the control case on the relevant physical components and flow structures was investigated in detail. The mode-competition process was illustrated to help understand the formation mechanism of the bistable flow. In particular, the total-dynamic-mode-decomposition reconstruction approach was adopted to recover the flow structures through superposing the zeroth mode and the different dominant modes. As a result, the individual vortex-shedding mode could be effectively isolated from the bistable flow by the total dynamic mode decomposition.

Criterion for vortex acoustic lock-on in combustors with backward facing step

In thermoacoustic systems vortex separation and breakdown are an important source of heat release rate fluctuations. The coupling between the acoustic field and the energy released by vortex breakdown can cause instability in these systems under certain operating conditions. Non-linear simulations show that combustion instability occurs after vortex acoustic lock-on. The objective of this work is to determine the criterion for vortex acoustic lock-on and thus the criterion for combustion instability as well. The 0-to-peak amplitude of the velocity fluctuations in the system are used as a criterion to determine the transition of Helmholtz number from vortex shedding mode to acoustic mode. Helmholtz number and acoustic pressure fluctuations computed using the model are compared with experimental investigations. The phenomenological model shows a good agreement with the experiments and the criterion determined for vortex lock-on provides a better understanding of the phenomenon.

Experimental study on laminar flow over two confined isothermal cylinders in tandem during mixed convection

An experimental investigation of laminar aiding and opposing mixed convection is carried out using particle image velocimetry (PIV) to assess the thermal effects on the wake of two isothermal cylinders of equal diameter in tandem array placed horizontally and confined inside a vertical closed-loop downward rectangular water channel. The buoyancy effect on the flow distributions are revealed for flow conditions with Reynolds number based on cylinder diameter of Re = 100 and 200, blockage ratio of BR = D/H = 0.3, aspect ratio of AR = W/D = 5, pitch-to-diameter ratio of σ=L/D = 3, and values of the buoyancy parameter (Richardson number) in the range −1≤Ri≤ 3. In this work, the interference effects on the complex flow features are presented in the form of mean and instantaneous contours of velocity and vorticity. In addition, separation angles, wake structure, recirculation bubble lengths, time traces of velocity fluctuation, Strouhal number and vortex shedding modes of the two-cylinder system are obtained as a function of the Richardson number. In this arrangement, the results indicate that the effects of the Reynolds number are very pronounced, and that the vortex shedding patterns exhibit a strong dependence on Ri. We also show the modulation effect of the channel walls on the three-dimensional flow under varying thermal buoyancy, and the results reported herein demonstrate how the flow structure, wake behavior and vortex shedding pattern are entirely different from that behind a single circular cylinder under wall confinement and thermal effects.

Reduced-order analysis of buffet flow of space launchers

A reduced-order analysis based on optimized dynamic mode decomposition (DMD) is performed on the turbulent wake of a generic axisymmetric space launcher configuration computed via a zonal large-eddy simulation at the free stream Mach number $Ma_{\infty }=0.8$ and the Reynolds number based on the main body diameter $Re_{D}=6\times 10^{5}$ to investigate the buffet phenomenon. The transonic wake is characterized by an unsteady recirculation region occurring around the nozzle due to the separation of the turbulent boundary layer at the main body shoulder and subsequent dynamic interaction of the unstable free-shear layer with the nozzle surface. This results in strongly periodic and antisymmetric wall pressure fluctuations, for which three distinct frequency ranges are identified using conventional spectral analysis, i.e. $Sr_{D}\approx 0.1$, $Sr_{D}\approx 0.2$ and $Sr_{D}\approx 0.35$. For the spatially integrated side (buffet) loads on the nozzle, the second range is found to be energetically most dominant. To clarify the origin of the detected wake dynamics, the underlying spatio-temporal coherent modes are extracted using DMD. Subsequent analysis of the reduced-order modelled flow field based on the identified DMD modes reveals that at $Sr_{D}\approx 0.1$ a longitudinal cross-pumping motion of the separation bubble takes place, caused by a harmonic antisymmetric oscillation of the main recirculation vortex in the streamwise direction. At $Sr_{D}\approx 0.2$, a cross-flapping motion of the shear layer is determined, triggered by antisymmetric vortex shedding which is in phase with the cross-pumping motion such that it occurs at twice the frequency value. The last range of $Sr_{D}\approx 0.35$ is attributed to a swinging motion of the shear layer caused by a higher harmonic of the vortex shedding mode. Conclusively, the controversial aspect of the true three-dimensional shape of the antisymmetric mode at $Sr_{D}\approx 0.2$ that dominates the buffet phenomenon is scrutinized. Inclined elongated closed-loop vortices are identified that are shed in alternating sequence from azimuthally opposite positions in a longitudinal plane of symmetry that changes its momentary orientation irregularly, maintaining an axisymmetric time-averaged field and spatially isotropic buffet loads.

Numerical simulation of vortex induced vibrations of a flexibly mounted wavy cylinder at subcritical Reynolds number

Wavy cylinders have been proven effective in controlling the flow and reducing the fluid induced forces. However, the hydro-elastic behavior of a flexibly mounted wavy cylinder remains unclear. The current paper endeavours to present a systematic study of the flow around a spring mounted wavy cylinder mainly at a moderate Reynolds number of 5000, the results of which are compared with a normal cylinder with the same fluid and structural attributions. It is discovered that the wavy cylinder, although almost eliminates the Kármán vortices in the fixed configuration, shows only limited efficacy on the mitigation of the flow induced vibration in the case of zero structural damping, and the typical initial-upper-lower type response curve is manifested. The hydrodynamic forces of the wavy cylinder also magnify significantly in the flexibly mounted cases during synchronization. Moreover, the phase lag between the lift coefficient and the displacement displays a clear change from 0° at the initial branch to 180° at the lower branch. The association of the 2S and 2P vortex shedding modes to the different branches is also similar to that of the normal cylinder, in which the 2S mode corresponds to the initial branch and the 2P to the lower branch. In general, despite the absence of the primary shedding frequency in the fixed configuration, the flexibly mounted wavy cylinder exhibits many features that is also found in the normal cylinder. This implies that the vortex induced vibration may not be initiated by the Kármán vortex shedding, and thus may defy the conventional view on the mechanism of the vortex induced vibrations. Additional simulations are performed with non-zero structural damping. It is disclosed that with sufficiently high structural damping, the vibration of the wavy cylinder could be reduced more efficiently than the normal cylinder.

Investigation on the vortex-and-wake-induced vibration of a separated-box bridge girder

Experiments are performed on three spring-supported separated-box girder section models in a closed wind tunnel to investigate the vortex-induced vibration (VIV) characteristics. A particle image velocimetry (PIV) instrument is employed to obtain the flow field around the models. Four VIV-sensitive velocity intervals are observed for the test model, in which vertical and torsional oscillations are repeatedly induced. Comparisons with the control groups show that vortex shedding in the gap is the crucial factor that induces VIVs. Wake-induced vibration (WIV) is observed to occur with VIV in the gap, accompanied by a dramatic magnification in vibrational amplitude. The WIV becomes weaker and disappears as the wind velocity increases, and the wake vortex-shedding mode changes from the classic 2S mode to a 2(2S) mode. The vortex-shedding frequency shows that it is a special lock-in mode of 1:2 phase-locking, which is found by taking the vibrating model and vortex-shedding as two coupled oscillators.

Numerical simulation of viscous flow past an oscillating square cylinder using a CIP-based model

The flow past an in-line forced oscillating square cylinder at Reynolds number of 200 is studied using an in-house code, named constrained interpolation profile method developed in Zhejiang University (CIP-ZJU). The model is established in the Cartesian coordinate system using the CIP method to discretise the Navier-Stokes equations. The fluid-structure interaction is treated as a multiphase flow of the liquid and solid phases to be solved simultaneously. An immersed boundary method is used to deal with the boundary of the solid body. The CFD model is first applied to the computation of the flow past a fixed square cylinder for its validation. Computations are then performed for the flow past a square cylinder oscillating in the streamwise direction. Considerable attention is paid to the symmetric and anti-symmetric modes of the vortex shedding in the oscillating square cylinder wake. Various oscillation amplitudes and frequencies are simulated and their effects on the vortex shedding modes are analyzed via Lissajous patterns of the unsteady lift coefficient. The relationship among the lift coefficient, the drag coefficient and the lock-on range is also investigated quantitatively.

Resonance in flow past oscillating cylinder under subcritical conditions

Flow around an oscillating cylinder in a subcritical region are numerically studied with a lattice Boltzmann method (LBM). The effects of the Reynolds number, oscillation amplitude and frequency on the vortex wake modes and hydrodynamics forces on the cylinder surface are systematically investigated. Special attention is paid to the phenomenon of resonance induced by the cylinder oscillation. The results demonstrate that vortex shedding can be excited extensively under subcritical conditions, and the response region of vibration frequency broadens with increasing Reynolds number and oscillation amplitude. Two distinct types of vortex shedding regimes are observed. The first type of vortex shedding regime (VSR I) is excited at low frequencies close to the intrinsic frequency of flow, and the second type of vortex shedding regime (VSR II) occurs at high frequencies with the Reynolds number close to the critical value. In the VSR I, a pair of alternately rotating vortices are shed in the wake per oscillation cycle, and lock-in/synchronization occurs, while in the VSR II, two alternately rotating vortices are shed for several oscillation cycles, and the vortex shedding frequency is close to that of a stationary cylinder under the critical condition. The excitation mechanisms of the two types of vortex shedding modes are analyzed separately.

On the unsteady wake dynamics behind a circular disk using fully 3D proper orthogonal decomposition

In the present work, the wakes behind a circular disk at various transitional regimes are numerically explored using fully 3D proper orthogonal decomposition (POD). The Reynolds numbers considered in this study (Re = 152, 170, 300 and 3000) cover four transitional states, i.e. the reflectional-symmetry-breaking (RSB) mode, the standing wave (SW) mode, a weakly chaotic state, and a higher-Reynolds-number state. Through analysis of the spatial POD modes at different wake states, it is found that a planar-symmetric vortex shedding mode characterized by the first mode pair is persistent in all the states. When the wake develops into a weakly chaotic state, a new vortex shedding mode characterized by the second mode pair begins to appear and completely forms at the higher-Reynolds-number state of Re = 3000, i.e. planar-symmetry-breaking vortex shedding mode. On the other hand, the coherent structure at Re = 3000 extracted from the first two POD modes shows a good resemblance to the wake configuration in the SW mode, while the coherent structure reconstructed from the first four POD modes shows a good resemblance to the wake configuration in the RSB mode. The present results indicate that the dynamics or flow instabilities observed at transitional RSB and SW modes are still preserved in a higher-Reynolds-number regime.