On the frequency selection of finite-amplitude vortex shedding 
in the cylinder wake

Pier, Benoı̂t

doi:10.1017/s0022112002008054

Cited by 176 publications

(209 citation statements)

References 33 publications

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“…The asymmetry in the vortex street pattern is characteristic of the frontal regime and does not occur in the quasigeostrophic regime where both cyclones and anticyclones have about the same size and shape even when the base velocity profile is asymmetric. Note that for the incompressible 2D wake 25 or for the present quasigeostrophic wake, since the perturbations are selfsustained due to the presence of an absolutely unstable region downstream of the cylinder, a local temporal analysis predicts an estimate of the Strouhal number three to four times too large. Hence, this strongly suggests a change in the nature of the wake instability when the geopotential fluctuations become large enough.…”

Section: Discussionmentioning

confidence: 76%

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Stability of parallel wake flows in quasigeostrophic and frontal regimes

et al. 2006

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International audienceRecent laboratory experiments [G. Perret, A. Stegner, M. Farge, and T. Pichon, Phys. Fluids 18, 036603 (2006)] have shown that the vortex-street formed in the wake of a towed cylinder in a rotating shallow-water layer could present a strong cyclone-anticyclone asymmetry. In extreme cases, only large-scale anticyclones were observed in the far wake. This asymmetry occurs in the so-called frontal regime when the Rossby number is small and the surface deviation is large. This asymmetry may have various origins and in particular may be attributed to the asymmetry of the flow around the cylinder, to the linear stability property of the wake, or to its nonlinear evolution. To discriminate between these mechanisms, we study the stability of two idealized parallel flows in the quasigeostrophic and in the frontal regimes. These parallel flows correspond to two velocity profiles measured just behind the cylinder in a region where the perturbations are negligible. According to our linear stability analysis, the most unstable mode, in the frontal regime, is localized in the anticyclonic shear region whether the base flow profile is symmetric or not. On a linear basis, it is thus more the instability that imposes the asymmetry than the base flow. Direct numerical simulations of the synthetic parallel wake flows show that nonlinearity exacerbates the dominance of the anticyclonic mode linearly selected. By numerically studying the spatio-temporal evolution of a small perturbation localized in space, we show that, unlike incompressible two-dimensional wake flows and the symmetric wake in the quasigeostrophic regime, the parallel asymmetric wake is strongly convectively unstable in the frontal regime, and not absolutely unstable. When the surface deformation becomes large, the wake instability changes from the absolute instability in the quasi-geostrophic regime to the strongly convective instability of the frontal regime. This explains well the changes. © 2006 American Institute of Physics

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Section: Discussionmentioning

confidence: 76%

“…In that incompressible case, Pier 25 showed that the wake flow is locally convectively unstable just behind the cylinder. This convectively unstable zone ends in the streamwise direction at x = 0.2D approximately while further down an absolutely unstable zone is present.…”

Section: Absolute/convective Instabilitymentioning

confidence: 99%

Stability of parallel wake flows in quasigeostrophic and frontal regimes

et al. 2006

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“…Barkley (2006) reports that a linear global stability analysis can still satisfactorily predict the shedding frequency well above the instability threshold provided it is performed on the time-averaged mean flow, not the base flow. This is somehow reminiscent of Hammond & Redekopp (1997) and Pier (2002), who early noticed that a linear criterion applied to the mean flow was remarkably successful in predicting the frequency of the unsteadiness in the frame of local stability analyses. In addition, Barkley (2006) shows that the mean flow is almost neutrally stable.…”

Section: Introductionmentioning

confidence: 83%

A self-consistent formulation for the sensitivity analysis of finite-amplitude vortex shedding in the cylinder wake

2016

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We use the adjoint method to compute sensitivity maps for the limit-cycle frequency and amplitude of the Bénard-von Kármán vortex street in the wake of a circular cylinder. The sensitivity analysis is performed in the frame of the semi-linear self-consistent model recently introduced by Mantič et al. (Phys. Rev. Lett. 2014; vol.113; 084501), which allows to describe accurately the effect of the control on the mean flow, but also on the finite-amplitude fluctuation that couples back nonlinearly onto the mean flow via the formation of Reynolds stress. The sensitivity is computed with respect to arbitrary steady and synchronous time-harmonic body forces. For small amplitude of the control, the theoretical variations of the limit-cycle frequency predict well those of the controlled flow, as obtained from either self-consistent modeling or direct numerical simulation of the Navier-Stokes equations. This is not the case if the variations are computed in the simpler mean flow approach overlooking the coupling between the mean and fluctuating components of the flow perturbation induced by the control. The variations of the limitcycle amplitude (that falls out the scope of the mean flow approach) are also correctly predicted, meaning that the approach can serve as a relevant and systematic guideline 2 P. Meliga, E. Boujo and F. Gallaire to control strongly unstable flows exhibiting non-small, finite amplitudes of oscillation.As an illustration, we apply the method to control by means of a small secondary control cylinder and discuss the obtained results in the light of the seminal experiments of Strykowski

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“…The success of this semi-empirical approach was demonstrated by various investigations, revealing that linear stability analysis is a powerful tool to model large-scale coherent structures in turbulent flows. Accordingly, this method can be applied at different degrees of complexity and accuracy, ranging from local stability analysis (Gaster et al 1985;Cohen & Wygnanski 1987a;Pier 2002;Juniper, Tammisola & Lundell 2011;Oberleithner et al 2011) through parabolized stability analysis (Herbert 1997;Gudmundsson & Colonius 2011) to global stability analysis (Barkley 2006;Meliga, Pujals & Éric 2012).…”

Section: Theoretical Conceptmentioning

confidence: 99%

On the impact of swirl on the growth of coherent structures

Oberleithner

Paschereit

Wygnanski³

2014

J. Fluid Mech.

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Spatial linear stability analysis is applied to the mean flow of a turbulent swirling jet at swirl intensities below the onset of vortex breakdown. The aim of this work is to predict the dominant coherent flow structure, their driving instabilities and how they are affected by swirl. At the nozzle exit, the swirling jet promotes shear instabilities and, less unstable, centrifugal instabilities. The latter stabilize shortly downstream of the nozzle, contributing very little to the formation of coherent structures. The shear mode remains unstable throughout generating coherent structures that scale with the axial shear-layer thickness. The most amplified mode in the nearfield is a co-winding double-helical mode rotating slowly in counter-direction to the swirl. This gives rise to the formation of slowly rotating and stationary large-scale coherent structures, which explains the asymmetries in the mean flows often encountered in swirling jet experiments. The co-winding single-helical mode at high rotation rate dominates the farfield of the swirling jet in replacement of the co-and counter-winding bending modes dominating the non-swirling jet. Moreover, swirl is found to significantly affect the streamwise phase velocity of the helical modes rendering this flow as highly dispersive and insensitive to intermodal interactions, which explains the absence of vortex pairing observed in previous investigations. The stability analysis is validated through hot-wire measurements of the flow excited at a single helical mode and of the flow perturbed by a time-and space-discrete pulse. The experimental results confirm the predicted mode selection and corresponding streamwise growth rates and phase velocities.

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On the frequency selection of finite-amplitude vortex shedding in the cylinder wake

Cited by 176 publications

References 33 publications

Stability of parallel wake flows in quasigeostrophic and frontal regimes

Stability of parallel wake flows in quasigeostrophic and frontal regimes

A self-consistent formulation for the sensitivity analysis of finite-amplitude vortex shedding in the cylinder wake

On the impact of swirl on the growth of coherent structures

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