Strouhal Frequency Research Articles

Unsteady RANS computations of flow around a circular cylinder for a wide range of Reynolds numbers

A methodology for computation of flow around circular cylinders is developed and tested using prominent commercial and open-source solvers; ANSYS® CFX-13.0 and OpenFOAM® 1.7.1 respectively. A range of diameters and flow conditions are accounted for by generating solutions for flows at Reynolds numbers ranging from 40 to 106. To maintain practical solve times a 2D Unsteady Reynolds-Averaged Navier–Stokes (URANS) approach is taken. Furthermore, to maximise accuracy a tightly controlled meshing methodology, suitable adaptive timestepping, and appropriate turbulence modelling, are assembled. The resulting data is presented for lift and drag forces, Strouhal frequency, time accuracy and boundary layer correlation. Despite closely matching case definitions, significant differences are found in the results between solvers; OpenFOAM displays high correlation with experimental data at low to sub-critical values, whereas ANSYS proves to be more effective in the high sub-critical and critical regions. This variance demonstrates the sensitivity of the case to solver specific mathematical constraints and that for practical engineering a parameter study is essential. By removing many common variances associated with grid and transient components of URANS computations the developed methodology can be used as a benchmark case for further codes solving cylindrical structures.

A Data-Driven Mode Identification Algorithm for Riser Fatigue Damage Assessment

A well-established empirical procedure, which we refer to as weighted waveform analysis (WWA), is employed to reconstruct a model riser's response over its entire length using a limited number of strain measurements. The quality of the response reconstruction is controlled largely by identification of the participating riser response modes (waveforms); hence, mode selection is vital in WWA application. Instead of selecting a set of consecutive riser vibratory modes, we propose a procedure that automatically identifies a set of nonconsecutive riser modes that can thus account for higher harmonics in the riser response (at multiplies of the Strouhal frequency). Using temporal data analysis of the discrete time-stamped samples, significant response frequencies are identified on the basis of power spectrum peaks; similarly, using the spatial data analysis of the sparse nonuniformly sampled data, significant wavenumbers are identified using Lomb–Scargle periodograms. Knowing the riser length, the most important wavenumber is related to a specific mode number; this dominant mode is, in turn, related to the dominant peak in power spectra based on the temporal data analysis. The riser's fundamental frequency is estimated as the ratio of the empirically estimated dominant spectral frequency to the dominant mode number. Additional mode numbers are also identified as spectral peak frequencies divided by the fundamental frequency. This mode selection technique is an improvement over similar WWA procedures that rely on a priori knowledge of the riser's fundamental frequency or on the knowledge of the physical properties and assumptions on added mass contributions. At selected target locations, we compare fatigue damage rates, estimated based on the riser response reconstructed using the WWA method with the proposed automated mode selection technique (we refer to this as the “improved” WWA) and those based on the “original” WWA method (that relies on a theoretically computed fundamental natural frequency of the riser). In both cases, predicted fatigue damage rates based on the empirical methods and data at various locations (other than the target) are cross-validated against damage rates based directly on measurements at the target location. The results show that the improved WWA method, which empirically estimates the riser's fundamental natural frequency and automatically selects significant modes of vibration, may be employed to estimate fatigue damage rates quite well from limited strain measurements.

Wake states and frequency selection of a streamwise oscillating cylinder

AbstractThis paper presents the results of an in-depth study of the flow past a streamwise oscillating cylinder, examining the impact of varying the amplitude and frequency of the oscillation, and the Reynolds number of the incoming flow. These findings are presented in a framework that shows that the relationship between the frequency of vortex shedding ${f}_{s} $ and the amplitude of oscillation ${A}^{\ast } $ is governed by two primary factors: the first is a reduction of ${f}_{s} $ proportional to a series in ${A}^{\ast 2} $ over a wide range of driving frequencies and Reynolds numbers; the second is nonlinear synchronization when this adjusted ${f}_{s} $ is in the vicinity of $N= {(1- {f}_{s} / {f}_{d} )}^{- 1} $, where $N$ is an integer. Typically, the influence of higher-order terms is small, and truncation to the first term of the series (${A}^{\ast 2} $) well represents the overall trend of vortex shedding frequency as a function of amplitude. However, discontinuous steps are overlaid on this trend due to the nonlinear synchronization. When ${f}_{s} $ is normalized by the Strouhal frequency ${f}_{St} $ (the frequency of vortex shedding from an unperturbed cylinder), the rate at which ${f}_{s} / {f}_{St} $ decreases with amplitude, at least for ${f}_{d} / {f}_{St} = 1$, shows a linear dependence on the Reynolds number. For a fixed $\mathit{Re}= 175$, the truncated series shows that the rate of decrease of ${f}_{s} / {f}_{St} $ with amplitude varies as ${(2- {f}_{d} / {f}_{St} )}^{- 1/ 2} $ for $1\leqslant {f}_{d} / {f}_{St} \leqslant 2$, but is essentially independent of ${f}_{d} / {f}_{St} $ for ${f}_{d} / {f}_{St} \lt 1$. These trends of the rate of decrease of ${f}_{s} $ with respect to amplitude are also used to predict the amplitudes of oscillation around which synchronization occurs. These predicted amplitudes are shown to fall in regions of the parameter space where synchronized modes occur. Further, for the case of varying ${f}_{d} / {f}_{St} $, a very reasonable prediction of the amplitude of oscillation required for the onset of synchronization to the mode where ${f}_{s} = 0. 5{f}_{d} $ is given. In a similar manner, amplitudes at which ${f}_{s} = 0$ are calculated, predicting where the natural vortex shedding is completely supplanted by the forcing. These amplitudes are found to coincide approximately with those at which the onset of a symmetric vortex shedding mode is observed. This result is interpreted as meaning that the symmetric shedding mode occurs when the dynamics crosses over from being dominated by the vortex shedding to being dominated by the forcing.

Mode competition in streamwise-only vortex induced vibrations

Time-resolved Particle-Image Velocimetry (PIV) has been used to study mode competition and transient behaviour in the wake of a cylinder experiencing Vortex-Induced Vibrations (VIV) in the streamwise direction. The cylinder response regime contained two branches, occurring above and below the onset of synchronisation between the wake and the cylinder motion (lock-in). During the first branch, the wake exhibited both the S-I mode (in which two vortices are shed simultaneously per vibration cycle) and the alternate A-II mode (similar to the well known von Kármán vortex street). An extended PIV data set acquired in this region revealed mode switching between the S-I and A-II modes. A criterion based on Proper-Orthogonal Decomposition was developed to identify which mode was dominant as a function of time. The A-II mode was found to be dominant for over 90% of the instantaneous fields examined, while the S-I mode appeared to be more unstable.Symmetrically shed vortices were found to rearrange downstream into an alternate structure in which the wake was no longer synchronised to the cylinder motion. The dominant frequency of transverse velocity fluctuations was measured throughout the wake in order to study the effects of this breakdown in more detail. For the majority of the wake, the fluctuations occurred at the Strouhal frequency, while in a region in the near wake the fluctuations occurred at the frequency of the cylinder motion. It is thought that during the first response branch vortices are formed at the cylinder response frequency, but tend to quickly rearrange downstream into an alternate structure which is no longer synchronised to the cylinder motion. As a result, the fluctuating drag will be synchronised to the structural motion, and is capable of providing positive energy transfer in the apparent absence of lock-in. Finally, the spatial dependence of the frequency of velocity fluctuations throughout the wake is used to explain some of the conflicting results in the literature regarding streamwise VIV, and the implications for the general study of VIV are discussed.

On vortex shedding from a hexagonal cylinder

The unsteady wake behind a hexagonal cylinder in cross-flow is investigated numerically. The time-dependent three-dimensional Navier–Stokes equations are solved for three different Reynolds numbers Re and for two different cylinder orientations. The topology of the vortex shedding depends on the orientation and the Strouhal frequency is generally higher in the wake of a face-oriented cylinder than behind a corner-oriented cylinder. For both orientations a higher Strouhal number St is observed when Re is increased from 100 to 500 whereas St is unaffected by a further increase up to Re=1000. The distinct variation of St with the orientation of the hexagonal cylinder relative to the oncoming flow is opposite of earlier findings for square cylinder wakes which exhibited a higher St with corner orientation than with face orientation.

Laboratory tests of vortex-induced vibrations of a long flexible riser pipe subjected to uniform flow

Laboratory tests have been conducted on vortex-induced vibration (VIV) of a long flexible riser towed horizontally in a wave basin. The riser model has an external diameter of 16 mm and a total length of 28.0 m giving an aspect ratio of about 1750. Reynolds numbers ranged from about 3000 to 10,000. Fiber optic grating strain gages are adopted to measure the dynamic response in both cross-flow and in-line directions. The cross-flow vibrations were observed to vibrate at modes up to 6 and the in-line reached up to 12. The fundamental response frequencies can be predicted by a Strouhal number of about 0.18. Multi-mode responses and the asymmetry of the bare pipe response in uniform flow were observed and analyzed. The experimental results confirmed that the riser pipe vibrated multi-modally despite it being subject to a uniform current profile and all of the excited modes vibrated at the Strouhal frequency. The asymmetrical distribution of displacement mainly resulted from the modal composition. Higher harmonics of the VIV response such as the third, fourth and fifth harmonics frequencies were found to be steady over the entire duration of the test even if they varied along the length of the riser pipe.

Vortex shedding and three-dimensional behaviour of flow past a cylinder confined in a channel

A numerical investigation of the flow past a circular cylinder centred in a two-dimensional channel of varying width is presented. For low Reynolds numbers, the flow is steady. For higher Reynolds numbers, vortices begin to shed periodically from the cylinder. In general, the Strouhal frequency of the shedding vortices increases with blockage ratio. In addition, a two-dimensional instability of the periodic vortex shedding is found, both empirically and by means of a Floquet stability analysis. The instability leads to a beating behaviour in the lift and drag coefficients of the cylinder, which occurs at a Reynolds number higher than the critical Reynolds number for the three-dimensional mode A-type instability, but lower than a Reynolds number for any mode B-type instability.

Luminescence from hydrodynamic cavitation

The majority of the research on cavitation luminescence has focused on the sonoluminescence or chemiluminescence generated by cavitation induced through ultrasound, with a lesser body of work on the luminescence induced by laser- or spark-induced cavitation. In such circumstances, the cavitation is generated in liquids where, on the broad scale, there is usually assumed to be no net liquid flow (although of course there are small-scale flows as a result of the cavitation itself, through radiation forces, streaming, microstreaming and turbulence). Little attention has been paid to the luminescence that accompanies (undesirable) cavitation in pumps and turbines or in marine propellers. In the present study, the sonoluminescence specific to air/water vapour bubbles, collapsing within a cavitation tunnel, is addressed. The particular case of leading edge cavitation over a two-dimensional hydrofoil is considered in detail. Hence, strong instabilities develop, causing the attached cavity to shed large clouds of micro bubbles. The spatial and temporal properties of the emitted luminescence were studied using an intensified charge coupled device video camera and a photomultiplier (PM). The light emission was found to extend downstream from the region of cavity closure, to the region where the travelling vortices collapse. Examination of the PM signal on short time scales showed that the emitted luminescence consisted of relatively intense flashes of short duration (as with other forms of luminescence). Individual flashes were often found to be clustered in time. Over longer time scales, clear evidence of periodicity was found in the PM signals. Further analysis showed that bursts of light were being emitted at the Strouhal frequency (for the shedding of transcient cavities).

Transition to turbulence in the separated shear layers of yawed circular cylinders

Spatial and temporal resolution of transition to turbulence inside the free-shear layers of two yawed circular cylinders is the subject of the present investigation. These physics were resolved using the large-eddy simulation (LES) methodology. An O-type grid was implemented such that the spatial scales of the LES computation fully resolved the energy range physics of the shear layers at Reynolds number Re D = 8000 based on the cylinder diameter. The two test cases modeled the cylinder span skewed at angles 45° and 60° from the horizontal axis. Observations revealed the same transition process as the normal cross-flow state. Soon after separation, Tollmien–Schlichting disturbances were predicted that evolved into Kelvin–Helmholtz (K–H) eddies before absorption by the large-scale Karman-type vortices. These eddies defaulted to a spanwise wavy pattern similar to a normal cross-flow due to their three-dimensional instability. No mixed modes were found between the K–H (Bloor) and Strouhal frequencies. The effect of yaw angle shortened the transition process. As a result, peak turbulence levels inside the wake formation zone approach the downstream cylinder periphery. In addition, the dimensionless frequencies of the K–H eddies lie above the normal cross-flow relationship as formulated by Bloor (1964). Disparity between the yawed and normal cross-flow states was further emphasized by the shear-layer transition characteristics. Although each property displayed the expected exponential growth during transition to turbulence, their dimensionless form was miss-aligned with those of the normal cross-flow case. Based on the present evidence, additional simulations (and/or experimental measurements) are necessary to form conclusive arguments regarding the expected behavior of the transition characteristics within the free-shear layers of yawed circular cylinders.

A numerical algorithm coupling a bifurcating indicator and a direct method for the computation of Hopf bifurcation points in fluid mechanics

This paper deals with the computation of Hopf bifurcation points in fluid mechanics. This computation is done by coupling a bifurcation indicator proposed recently (Cadou et al., 2006) [1] and a direct method (Jackson, 1987; Jepson, 1981) [2,3] which consists in solving an augmented system whose solutions are Hopf bifurcation points. The bifurcation indicator gives initial critical values (Reynolds number, Strouhal frequency) for the direct method iterations. Some classical numerical examples from fluid mechanics, in two dimensions, are studied to demonstrate the efficiency and the reliability of such an algorithm.

Contrasting the Cartesian and polar forms of the shedding-induced force vector in response to 12 subharmonic and superharmonic mechanical excitations

We mechanically excited the near-field shedding of the von Kármán vortex street of a stationary cylinder at Reynolds number 300 by moving it sinusoidally with 12 different frequencies. We first solved the incompressible Navier–Stokes equations using the finite difference method and obtained unexcited shedding, which occurs at the Strouhal frequency. Then, we applied six subharmonic excitations with rational frequency ratios (defined as the excitation frequency to the Strouhal frequency) in the form 1/n and six superharmonic excitations with frequency ratios n, where n is an integer taking values between 2 and 7. We compared the behavior of the shedding-induced force vector acting on the cylinder in each excitation case to their counterparts in the other excitation cases and to the case of the stationary cylinder. This force vector has two representations: lift and drag (Cartesian) or magnitude and direction (polar). Whereas the first representation is commonly used in theoretical fluid mechanics and engineering applications, we found that the second representation is favored in terms of revealing how the force vector responds to the applied excitations. For example, the mean and standard deviation of the drag do not show clear trends with the excitation frequency, whereas the force magnitude changes quadratically with it. We showed that the theoretical analysis of a simplified nonlinear wake model does in fact support this behavior. We found three modes of shedding-induced force in response to mechanical excitation, depending on the ratio of excitation frequency to Strouhal frequency. Near-field shedding is not entrained by excitation for all subharmonic excitations, but it is entrained for all superharmonic excitations. For entrained shedding, we found two behaviors of the shedding-induced force vector, which is periodic only at odd frequency ratios.

Dual resonance in vortex-induced vibrations at subcritical and supercritical Reynolds numbers

An experimental study is performed on the vortex induced vibrations of a rigid flexibly mounted circular cylinder placed in a crossflow. The cylinder is allowed to oscillate in combined crossflow and in-line motions, and the ratio of the nominal in-line and transverse natural frequencies is varied systematically. Experiments were conducted on a smooth cylinder at subcritical Reynolds numbers between 15 000 and 60 000 and on a roughened cylinder at supercritical Reynolds numbers between 320 000 and 710 000, with a surface roughness equal to 0.23 % of the cylinder diameter. Strong qualitative and quantitative similarities between the subcritical and supercritical experiments are found, especially when the in-line natural frequency is close to twice the value of the crossflow natural frequency. In both Reynolds number regimes, the test cylinder may exhibit a ‘dual-resonant’ response, resulting in resonant crossflow motion at a frequencyfv, near the Strouhal frequency, and resonant in-line motion at 2fv. This dual resonance is shown to occur over a relatively wide frequency region around the Strouhal frequency, accompanied by stable, highly repeatable figure-eight cylinder orbits, as well as large third-harmonic components of the lift force. Under dual-resonance conditions, both the subcritical and the supercritical response is shown to collapse into a narrow parametric region in which the effective natural-frequency ratio is near the value 2, regardless of the nominal natural-frequency ratio. Some differences are noted in the magnitudes of forces and the cylinder response between the two different Reynolds number regimes, but the dual-resonant response and the resulting force trends are preserved despite the large Reynolds number difference.

Chaos in a cylinder wake due to forcing at the Strouhal frequency

In this letter we show that a cylinder oscillating harmonically in line with an incoming flow at a frequency equal to the natural frequency of vortex shedding induces for certain amplitudes of oscillation a chaotic state in the flow, characterized by an aperiodic lift force. The result is obtained through numerical simulation of the Navier–Stokes equations for two-dimensional flow. The chaos is attributed to the competition between two modes: the natural mode of the wake and the mode forced by the moving cylinder, which have entirely different spatial structures.

Optimal Vortex Formation as a Unifying Principle in Biological Propulsion

I review the concept of optimal vortex formation and examine its relevance to propulsion in biological and bio-inspired systems, ranging from the human heart to underwater vehicles. By using examples from the existing literature and new analyses, I show that optimal vortex formation can potentially serve as a unifying principle to understand the diversity of solutions used to achieve propulsion in nature. Additionally, optimal vortex formation can provide a framework in which to design engineered propulsions systems that are constrained by pressures unrelated to biology. Finally, I analyze the relationship between optimal vortex formation and previously observed constraints on Strouhal frequency during animal locomotion in air and water. It is proposed that the Strouhal frequency constraint is but one consequence of the process of optimal vortex formation and that others remain to be discovered.

How fast can a river flow over alluvium?

A new “vortex–drag” approach is proposed to compute the rate of dissipation of mean–motion energy in alluvial streams flowing over mobile bed forms. 1D–routing exercises strongly suggest that, for a given depth and energy–slope, there exists a certain flow velocity limit an alluvial stream is unlikely to exceed. This remarkable flow condition would actually correspond to a fundamental mode in terms of vortex Strouhal frequency (to which only higher harmonics can eventually be associated). Interestingly, the maximum possible velocity is not attained over a plane bed, but occurs when the wavy shape of the water–surface remains in phase with the sand wave. The model treats flow over sandy alluvium as a combination of boundary–attached and –detached flow features, both necessary to explain how well–marked protrusions can develop spontaneously in the bed profile and be maintained in response to extreme water–sediment discharge and stream power conditions. Through the vortex–drag concept and its mathematical development, a lot is learned about the nature of the mutual interactions existing between the various alluvial processes: bedform development, alluvial channel resistance, sediment transport capacity and turbulence–damping. Bedform types occurring in the upper alluvial regime are at the center of the analysis. Based on the model and on confrontation with available experimental evidence, it is suggested that the inphase wave [IPW] flow configuration is associated with minimum possible drag, creating low–turbulence high–velocity conditions ideal to evacuate extreme river discharges. Occurrence of IPW conditions is therefore important in terms of flooding alleviation, but will develop only if the right type of sediment is maintained available on the stream bed. The boundary–attached component of the model introduces a generalized Froude number formulation in alluvial hydraulics, to represent topographically–forced gravity waves occurring in non–shallow environments such as ripple fields. For the boundary–detached component of the model, we introduce a “control factor m” (m ≥ 1) which reflects a complex feedback–control loop process active in the separation cell immediately downstream of the bedform crest. Lift–up of bed particles (under the action of the corresponding vortices shedding out of the reattachment region) implies that control factor m should also play an important role in the further development of bursting–based conceptual models of non–cohesive sediment transport.

Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number: Forced and free oscillations

A numerical simulation of the flow past a circular cylinder which is able to oscillate transversely to the incident stream is presented in this paper for a fixed Reynolds number equal to 100. The 2D Navier–Stokes equations are solved by a finite volume method with an industrial CFD code in which a coupling procedure has been implemented in order to obtain the cylinder displacement. A preliminary work is first conducted for a fixed cylinder to check the wake characteristics for Reynolds numbers smaller than 150 in the laminar regime. The Strouhal frequency f S and the aerodynamic coefficients are thus controlled among other parameters. Simulations are then performed with forced oscillations characterized by the frequency ratio F = f 0/ f S, where f 0 is the forced oscillation frequency, and by the adimensional amplitude A. The wake characteristics are analyzed using the time series of the fluctuating aerodynamic coefficients and their power spectral densities (PSD). The frequency content is then linked to the shape of the phase portraits and to the vortex shedding mode. By choosing interesting couples ( A, F), different vortex shedding modes have been observed, which are similar to those of the Williamson–Roshko map. A second batch of simulations involving free vibrations (so-called vortex-induced vibrations or VIV) is finally carried out. Oscillations of the cylinder are now directly induced by the vortex shedding process in the wake and therefore, the time integration of the motion is realized by an explicit staggered algorithm which provides the cylinder displacement according to the aerodynamic charges exerted on the cylinder wall. Amplitude and frequency response of the cylinder are thus investigated over a wide range of reduced velocities to observe the different phenomena at stake. In particular, the vortex shedding modes have also been related to the frequency response observed and our results at Re = 100 show a very good agreement with other studies using different numerical approaches.

Numerical simulation of laminar flow past a circular cylinder

The present paper focuses on the analysis of two- and three-dimensional flow past a circular cylinder in different laminar flow regimes. In this simulation, an implicit pressure-based finite volume method is used for time-accurate computation of incompressible flow using second order accurate convective flux discretisation schemes. The computation results are validated against measurement data for mean surface pressure, skin friction coefficients, the size and strength of the recirculating wake for the steady flow regime and also for the Strouhal frequency of vortex shedding and the mean and RMS amplitude of the fluctuating aerodynamic coefficients for the unsteady periodic flow regime. The complex three dimensional flow structure of the cylinder wake is also reasonably captured by the present prediction procedure.

Numerical simulation of vortex-induced vibration of a square cylinder

Vortex-induced vibration (VIV) of a square cylinder in a cross flow is examined numerically. Both the rigid and elastic cases are simulated at a low Reynolds number of 100. The approach solves the unsteady flow field using a finite element method with a deforming grid to accommodate the moving cylinders. As for the cylinder motions, a two-degree-of-freedom structural dynamics model is invoked. Fluid-structure interactions are resolved through iteration at the same time step. The calculated results for the case of rigid cylinder indicated that the non-dimensional vortex shedding frequency (or the Strouhal frequency) of a square cylinder at rest is 0.13, which is in good agreement with the published results. For the elastic case, with the change of the cylinder’s natural frequency, “lock-in” and “beat” phenomena were successfully captured. The phenomena of resonance and galloping can also be indicated.

Investigation of high frequency noise generation in the near-nozzle region of a jet using large eddy simulation

This paper reports on the simulation of the near-nozzle region of an isothermal Mach 0.6 jet at a Reynolds number of 100,000 exhausting from a round nozzle geometry. The flow inside the nozzle and the free jet outside the nozzle are computed simultaneously by a high-order accurate, multi-block, large eddy simulation (LES) code with overset grid capability. The total number of grid points at which the governing equations are solved is about 50 million. The main emphasis of the simulation is to capture the high frequency noise generation that takes place in the shear layers of the jet within the first few diameters downstream of the nozzle exit. Although we have attempted to generate fully turbulent boundary layers inside the nozzle by means of a special turbulent inflow generation procedure, an analysis of the simulation results supports the fact that the state of the nozzle exit boundary layer should be characterized as transitional rather than fully turbulent. This is believed to be most likely due to imperfections in the inflow generation method. Details of the computational methodology are presented together with an analysis of the simulation results. A comparison of the far field noise spectrum in the sideline direction with experimental data at similar flow conditions is also carried out. Additional noise generation due to vortex pairing in the region immediately downstream of the nozzle exit is also observed. In a second simulation, the effect of the nozzle exit boundary layer thickness on the vortex pairing Strouhal frequency (based on nozzle diameter) and its harmonics is demonstrated. The limitations and deficiencies of the present study are identified and discussed. We hope that the lessons learned in this study will help guide future research activities towards resolving the pending issues identified in this work.

Sensitivity of a Square Cylinder Wake to Forced Oscillations

The wake of a square cylinder at zero angle of incidence oscillating inline with the incoming stream has been experimentally studied. Measurement data are reported for Reynolds numbers of 170 and 355. The cylinder aspect ratio is set equal to 28 and a limited study at an aspect ratio of 16 has been carried out. The frequency of oscillation is varied around the Strouhal frequency of a stationary cylinder, and the amplitude of oscillation is 10–30% of the cylinder size. Spatial and temporal flow fields in the cylinder wake have been studied using particle image velocimetry and hot-wire anemometry, the former providing flow visualization images as well. A strong effect of forcing frequency is clearly seen in the near wake. With an increase in frequency, the recirculation length substantially reduces and diminishes the time-averaged drag coefficient. The time-averaged vorticity contours show that the large-scale vortices move closer to the cylinder. The rms values of velocity fluctuations increase in magnitude and cluster around the cylinder as well. The production of turbulent kinetic energy shows a similar trend as that of spanwise vorticity with the former showing greater asymmetry at both sides of the cylinder centerline. The instantaneous vorticity contours show that the length of the shear layer at separation decreases with increasing frequency. The effect of amplitude of oscillation on the flow details has been studied when the forcing frequency is kept equal to the vortex-shedding frequency of the stationary cylinder. An increase in amplitude diminishes the time-averaged drag coefficient. The peak value of rms velocity increases, and its location moves upstream. The length of the recirculation bubble decreases with amplitude. The reduction in drag coefficient with frequency and amplitude is broadly reproduced in experiments with the cylinder of lower aspect ratio.