Symmetry breaking of two-dimensional time-periodic wakes

Blackburn, Hugh Maurice; Marqués, Francisco; Lopez, Juan M.

doi:10.1017/s0022112004002095

Cited by 102 publications

(127 citation statements)

References 42 publications

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“…They showed that Mode-C appears in the near-wake of the downstream cylinder with an intermediate spanwise wavelength between Mode-A and Mode-B with a period-doubling character. The prevailing feature of the subharmonic Mode-C instability is that it can only be produced in flows which exhibit a breaking of the Z 2 spatio-temporal symmetry, Blackburn et al 12 The placement of a trip-wire near to a circular cylinder but offset from the wake centerline in our experiments serves to break this symmetry and permit the emergence of a subharmonic instability mode.…”

Section: Introductionmentioning

confidence: 71%

“…Subsequently, Sheard et al 10 provided additional computational results and the first experimental observations of the subharmonic mode Mode-C. Later, Sheard et al 11 showed that the period-doubling nature of the wake is maintained by a cycle of convection of the perturbation vorticity from the near-wake. A unified description of a time-periodic 2D flow with space-time reflection symmetry (such as the von Karman vortex street) bifurcating to a non-symmetric 3D flow, like the Mode-C transition, using a Floquet stability analysis is presented in Blackburn et al 12 and Blackburn and Sheard. 13 It is shown that the symmetry-breaking 3D transition of time-periodic wakes is not correlated with the physical characteristics such as the spanwise wavelength of the flows.…”

Section: Introductionmentioning

confidence: 99%

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Energy contents and vortex dynamics in Mode-C transition of wired-cylinder wake

2013

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The 3D transition of the flow behind a circular cylinder with a near-wake wire disturbance has been investigated experimentally. The flow is oriented horizontally and the wire is positioned in the upper half of the wake. We performed flow visualization and particle image velocimetry experiments to investigate the influence of the wire on various properties of the flow, such as the dynamics of the spanwise structures. Experiments were performed in the Reynolds number range of Re = 165–300. It is shown that in Mode-C transition of the wired cylinder wake, some part of the streamwise vorticity content of the upper von Kármán vortices located at the perturbed side, is transferred to the secondary vortices. This vorticity transfer results in upper von Kármán vortices which are weaker than the lower ones. The analysis of the discrete energy content of the wake supports this analysis by showing that the energy intensity at von Kármán vortex shedding frequency f0 at the perturbed side of the wake is less than the energy intensity in the lower half. This leads to conclusion that the excess energy is transferred to the subharmonic frequency f1 ≈ f0/2.

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Section: Introductionmentioning

confidence: 71%

Section: Introductionmentioning

confidence: 99%

Energy contents and vortex dynamics in Mode-C transition of wired-cylinder wake

2013

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“…The computational methods employed were previously described and applied in Blackburn (2002), Blackburn & Lopez (2002, 2003a, Blackburn & Sherwin (2004), Blackburn et al (2005) and Barkley, Blackburn & Sherwin (2008), and so only a brief overview is presented here.…”

Section: Methodsmentioning

confidence: 99%

Modulated waves in a periodically driven annular cavity

Blackburn

Lopez

2010

J. Fluid Mech.

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Time-periodic flows with spatio-temporal symmetry Z 2 × O(2) -invariance in the spanwise direction generating the O(2) symmetry group and a half-period-reflection symmetry in the streamwise direction generating a spatio-temporal Z 2 symmetry group -are of interest largely because this is the symmetry group of periodic laminar two-dimensional wakes of symmetric bodies. Such flows are the base states for various three-dimensional instabilities; the periodically shedding two-dimensional circular cylinder wake with three-dimensional modes A and B being the generic example. However, it is not easy to physically realize the ideal flows owing to the presence of end effects and finite spanwise geometries. Flows past rings are sometimes advanced as providing a relevant idealization, but in fact these have symmetry group O(2) and only approach Z 2 × O(2) symmetry in the infinite aspect ratio limit. The present work examines physically realizable periodically driven annular cavity flows that possess Z 2 × O(2) spatio-temporal symmetry. The flows have three distinct codimension-1 instabilities: two synchronous modes (A and B), and two manifestations of a quasi-periodic (QP) mode, either as modulated standing waves or modulated travelling waves. It is found that the curvature of the system can determine which of these modes is the first to become unstable with increasing Reynolds number, and that even in the nonlinear regime near onset of three-dimensional instabilities the dynamics are dominated by mixed modes with complicated spatio-temporal structure. Supplementary movies illustrating the spatio-temporal dynamics are available at journals.cambridge.org/flm.

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“…Experiments and numerical simulations have been conducted in these flows, looking for the three-dimensional dynamics after breaking the O(2) symmetry [3,4,7,8,15]. In these different settings, the analysis of the three-dimensional dynamics has faced different setbacks.…”

Section: Discussionmentioning

confidence: 99%

“…Furthermore, these flows have an additional space-time symmetry: a reflection about the wake centerline followed by a half-period temporal evolution. In several wake flows, two distinct synchronous modes that break into the spanwise direction (with real Floquet exponent) have been observed experimentally [1][2][3][4], computed as direct instabilities from the flow [2,[5][6][7][8], and studied theoretically [9][10][11]. These modes are associated with breaking or preserving the spatiotemporal symmetry.…”

Section: Introductionmentioning

confidence: 99%

Mode competition in cylindrical flows driven by sidewall oscillations

2013

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The transition from a two-dimensional to three-dimensional flow in systems with spatial O(2) symmetry and spatiotemporal Z 2 symmetry happens in many fluid systems, like wakes or periodically forced flows. In most of these systems, the dynamics after the first bifurcation is very complex and involves cascades of bifurcations in a very narrow parameter range. A numerical study of a flow in an enclosed cylindrical cavity driven by axial oscillations of the sidewall, which allows a detailed study of the secondary bifurcations and the corresponding mode interactions, is presented. The study focuses on a codimension-2 point that acts as the organizing center of the dynamics for moderate values of the forcing frequency. The unraveled dynamics is very rich, including slow-fast dynamics and hysteresis, and may help understand the bifurcation cascades in more complex systems.

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Symmetry breaking of two-dimensional time-periodic wakes

Cited by 102 publications

References 42 publications

Energy contents and vortex dynamics in Mode-C transition of wired-cylinder wake

Energy contents and vortex dynamics in Mode-C transition of wired-cylinder wake

Modulated waves in a periodically driven annular cavity

Mode competition in cylindrical flows driven by sidewall oscillations

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