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The flow behind rings: bluff body wakes without end effects
- T. Leweke, M. Provansal
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- Journal:
- Journal of Fluid Mechanics / Volume 288 / 10 April 1995
- Published online by Cambridge University Press:
- 26 April 2006, pp. 265-310
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Recent studies have demonstrated the strong influence of end effects on low-Reynoldsnumber bluff body wakes, and a number of questions remain concerning the intrinsic nature of three-dimensional phenomena in two-dimensional configurations. Some of them are answered by the present study which investigates the wake of bluff rings (i.e. bodies without ends) both experimentally and by application of the phenomenological Ginzburg–Landau model. The model turns out to be very accurate in describing qualitative and quantitative observations in a large Reynolds number interval. The experimental study of the periodic vortex shedding regime shows the existence of discrete shedding modes, in which the wake takes the form of parallel vortex rings or ‘oblique’ helical vortices, depending on initial conditions. The Strouhal number is found to decrease with growing body curvature, and a global expression for the Strouhal–Reynolds number relation, including curvature and shedding angle, is proposed, which is consistent with previous straight cylinder results. A secondary instability of the helical modes at low Reynolds numbers is discovered, and a detailed comparison with the Ginzburg–Landau model identifies it as the Eckhaus modulational instability of the spanwise structure of the near-wake formation region. It is independent of curvature and its clear observation in straight cylinder wakes is inhibited by end effects.
The dynamical model is extended to higher Reynolds numbers by introducing variable parameters. In this way the instability of periodic vortex shedding which marks the beginning of the transition range is characterized as the Benjamin–Feir instability of the coupled oscillation of the near wake. It is independent of the shear layer transition to turbulence, which is known to occur at higher Reynolds numbers. The unusual shape of the Strouhal curve in this flow regime, including the discontinuity at the transition point, is qualitatively reproduced by the Ginzburg–Landau model. End effects in finite cylinder wakes are found to cause important changes in the transition behaviour also: they create a second Strouhal discontinuity, which is not observed in the present ring wake experiments.
Bénard-von Kármán instability: transient and forced regimes
- M. Provansal, C. Mathis, L. Boyer
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- Journal:
- Journal of Fluid Mechanics / Volume 182 / September 1987
- Published online by Cambridge University Press:
- 21 April 2006, pp. 1-22
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The wake of a circular cylinder is investigated near the oscillation threshold by means of a laser probe. Above the threshold the transient regime is studied and described by a Stuart-Landau law (already found to be relevant in explaining free-oscillating regimes). Below the critical point, impulse and resonant regimes are examined, so the coefficients of the Stuart-Landau equation are determined.
Moreover, in the supercritical regime, the behaviour of the (externally forced) oscillating system is described, varying parameters such as threshold deviation, forcing frequency and amplitude. The different zones of entrainment and desynchronization are given for simple or harmonic frequency.
2 - Vortices
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- By J. M. Lopez, A. D. Perry, P. Koumoutsakos, A. Leonard, M. P. Escudier, G. J. F. Van Heijst, R. C. Kloosterziel, C. W. M. Williams, H. Higuchi, H. Balligand, M. Visbal, G. D. Miller, C. H. K. Williamson, H. Higuchi, F. M. Payne, R. C. Nelson, T. T. Ng, Q. Rahaman, A. Alvarez-Toledo, B. Parker, C. M. Ho, T. Leweke, M. Provansal, D. Ormières, R. Lebescond, J. C. Owen, A. A. Szewczyk, P. W. Bearman, G. J. F. Van Heijst, J. B. Flór, C. Seren, M. V. Melander, N. J. Zabusky, P. Petitjeans, R. Hancock
- M. Samimy, Ohio State University, K. S. Breuer, Brown University, Rhode Island, L. G. Leal, University of California, Santa Barbara, P. H. Steen, Cornell University, New York
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- Book:
- A Gallery of Fluid Motion
- Published online:
- 25 January 2010
- Print publication:
- 12 January 2004, pp 11-27
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Summary
Periodic axisymmetric vortex breakdown in a cylinder with a rotating end wall
When the fluid inside a completely filled cylinder is set in motion by the rotation of the bottom end wall, steady and unsteady axisymmetric vortex breakdown is possible. The onset of unsteadiness is via a Hopf bifurcation.
Figure 1 is a perspective view of the flow inside the cylinder where marker particles have been released from an elliptic ring concentric with the axis of symmetry near the top end wall. This periodic flow corresponds to a Reynolds number Re=2765 and cylinder aspect ratio H/R=2.5. Neighboring particles have been grouped to define a sheet of marker fluid and the local transparency of the sheet has been made proportional to its local stretching. The resultant dye sheet takes on an asymmetric shape, even though the flow is axisymmetric, due to the unsteadiness and the asymmetric release of marker particles.When the release is symmetric, as in Fig. 2, the dye sheet is also symmetric. These two figures are snapshots of the dye sheet after three periods of the oscillation (a period is approximately 36.3 rotations of the end wall). Figure 3 is a cross section of the dye sheet in Fig. 2 after 26 periods of the oscillation. Here only the marker particles are shown. They are colored according to their time of release, the oldest being blue, through green and yellow, and the most recently released being red. Comparison with Escudier's experiment shows very close agreement.
The particle equations of motion correspond to a Hamiltonian dynamical system and an appropriate.