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Stability properties of forced wakes

Published online by Cambridge University Press:  02 May 2007

B. THIRIA  and
J. E. WESFREID
B. THIRIA
Affiliation:
Physique et Mécanique des Milieux Hétérogènes, Ecole Supérieure de Physique et Chimie Industrielles de Paris (PMMH UMR 7636-CNRS; ESPCI; Paris 6; Paris 7), 10 rue Vauquelin, 75231 Paris Cedex 5, France
J. E. WESFREID
Affiliation:
Physique et Mécanique des Milieux Hétérogènes, Ecole Supérieure de Physique et Chimie Industrielles de Paris (PMMH UMR 7636-CNRS; ESPCI; Paris 6; Paris 7), 10 rue Vauquelin, 75231 Paris Cedex 5, France
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Abstract

Thiria, Goujon-Durand & Wesfreid (J. Fluid Mech. vol. 560, 2006, p. 123), it was shown that vortex shedding from a rotationally oscillating cylinder at moderate Reynolds number can be characterized by the spatial coexistence of two distinct patterns, one of which is related to the forcing frequency in the near wake and the other to a frequency close to the natural one for the unforced case downstream of this locked region. The existence and the modification of these wake characteristics were found to be strongly affected by the frequency and the amplitude of the cylinder oscillation. In this paper, a linear stability analysis of these forced regimes is performed, and shows that the stability characteristics of such flows are governed by a strong mean flow correction which is a function of the oscillation parameters. We also present experiments on the spatial properties of the global mode and on the selection of the vortex shedding frequency as a function of the forcing conditions for Re = 150. Finally, we elucidate a diagram of locked and non-locked states, for a large range of frequencies and amplitudes of the oscillation.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 579 , 25 May 2007 , pp. 137 - 161
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Baek, S.-J., Lee, S. B. & Sung, H. J. 2001 Response of a circular cylinder wake to superharmonic excitation. J. Fluid Mech. 442, 67–88.CrossRefGoogle Scholar
Baek, S.-J. & Sung, H. J. 2000 Quasi-periodicity in the wake of a rotationnally oscillating cylinder. J. Fluid Mech. 408, 275–300.CrossRefGoogle Scholar
Barkley, D., Gomes, M. G. M. & Henderson, R. D. 2002 Three dimensional instability in flow over a backward-facing step. J. Fluid Mech. 473, 167–190.CrossRefGoogle Scholar
Bénard, H. 1928 Sur les tourbillons alternés et la loi de similitude. C. R. Acad. Sci. 187, 1123–1125.Google Scholar
Camichel, C., Dupin, P. & Teissié-Solier, M. 1927 Sur l'application de la loi de similitude aux période de formation des tourbillons alternés de Bénard-Kàrmàn. C. R. Acad. Sci. 185, 1556–1559.Google Scholar
Cheng, M., Chew, Y. T. & Luo, S. C. 2001 Numerical investigation of a rotationally oscillating cylinder in mean flow. J. Fluids Struct. 15, 981–1007.CrossRefGoogle Scholar
Choi, S., Choi, H. & Kang, S. 2002 Characteristics of flow over a rotationally oscillating cylinder at low Reynolds number. Phys. Fluids 14, 2767–2777.CrossRefGoogle Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows. Annu. Rev. Fluid. Mech. 37, 357–392.CrossRefGoogle Scholar
Chomaz, J.-M., Huerre, P. & Redekopp, L. 1991 A frequency selection criterion in spatially developing flows. Stud. Appl. Maths 84, 119–144.CrossRefGoogle Scholar
Chou, M.-H. 1997 Synchronization of vortex shedding from a cylinder under rotary oscillation. Comput Fluids. 26, 755–774.CrossRefGoogle Scholar
Cooper, A. J. & Crighton, D. G. 2000 Global modes and superdirective acoustic radiation in low-speed axisymmetrics jets. Eur. J. Mech. B/Fluids 19, 559–574.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stabilities. Cambridge University Press.Google Scholar
Goujon-Durand, S., Jenffer, P. & Wesfreid, J. E. 1994 Downstream evolution of the Bénard-Von Karman instability. Phys. Rev. E 50, 308–313.Google ScholarPubMed
Hammond, D. & Redekopp, L. 1997 Global dynamics of symmetric and asymmetric wakes. J. Fluid Mech. 331, 231–260.CrossRefGoogle Scholar
Koch, W. 1985 Local instability charcteristics and frequency determination on self-exited wake flows. J. Sound Vib. 99, 53–83.CrossRefGoogle Scholar
Kupfer, K., Bers, A. & Ram, A. K. 1987 The cusp map in the complex-frequency plane for absolute instabilities. Phys. Fluids 30, 3075–3082.CrossRefGoogle Scholar
Le Dizes, S., Huerre, P., Chomaz, J.-M. & Monkewitz, P. 1996 Linear global modes in spatially develloping media. Phil. Trans. R. Soc. Lond. A 354, 169–212.Google Scholar
Lu, X.-Y. & Sato, J. 1996 A numerical study of flow past a rotationally oscillating circular cylinder. J. Fluids Struct. 10, 829–849.CrossRefGoogle Scholar
Mattingly, G. & Criminale, W. 1972 The stability of an incompressible two-dimensional wake. J. Fluid Mech. 51, 233–272.CrossRefGoogle Scholar
Nishihara, T., Kanedo, S. & Watanabe, T. 2005 Characteristics of fluid dynamic forces acting on a circular cylinder oscillating in the streamwise direction and its wake patterns. J. Fluids Struct. 20, 505–518.CrossRefGoogle Scholar
Noack, B., Afanasiev, K., Morzynski, M., Tadmor, G. & Thiele, F. 2003 A hierarchy of low dimensional models for the transient and post-transient cylinder wake. J. Fluid Mech. 497, 335–363.CrossRefGoogle Scholar
Pier, B. 2002 On the frequency selection of finite-amplitude vortex shedding in the cylinder wake. J. Fluid Mech. 458, 407–417.CrossRefGoogle Scholar
Pierrehumbert, R. 1984 Local and global baroclinic instability of zonally varying flow. J. Atmos. Sci. 41, 2141–2162.2.0.CO;2>CrossRefGoogle Scholar
Protas, B. 2000 Analyse et contrôle des forces hydrodynamiques d'un écoulement bidimentionnel derrière un obstacle en mouvement. Application de la méthode du vortex. PhD Thesis, Warsaw University of Technologiy, Poland, and Université Paris VI. Paris, France.Google Scholar
Protas, B. & Wesfreid, J. E. 2002 Drag force in the open-loop control of the cylinder wake in the laminar regime. Phys. Fluids 14, 810–826.CrossRefGoogle Scholar
Protas, B. & Wesfreid, J. E. 2003 On the relation between the global modes and the spectra of drag and lift in periodic wake flows. C. R. Méc. \331, 49–54.CrossRefGoogle Scholar
Provansal, M., Mathis, C. & Boyer, L. 1987 Bénard-Von Karman instability: transient and forced regimes. J. Fluid Mec 182, 1–22.CrossRefGoogle Scholar
Saffman, P. F. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Siggia, E. & Zippelius, A. 1981 Pattern selection in Rayleigh-Bénard convection. Phys. Rev. Lett. 47, 835–838CrossRefGoogle Scholar
Thiria, B. 2005 Propriétés dynamiques et de stabilité dans les écoulements ouverts forcés. PhD Thesis, Université Paris VI. Paris, France.Google Scholar
Thiria, B., Bouchet, G. & Wesfreid, J. E. 2007 Critical properties of forced wakes. In preparation.CrossRefGoogle Scholar
Thiria, B., Goujon-Durand, S. & Wesfreid, J. E. 2006 Wake of a cylinder performing rotary oscillation. J. Fluid Mech. 560, 123–147.CrossRefGoogle Scholar
Triantafyllou, G., Triantafyllou, M. & Chryssostomidis, C. 1986 On the formation of vortex street behind stationary cylinder. J. Fluid Mech. 170, 461–477.CrossRefGoogle Scholar
Wesfreid, J. E., Goujon-Durand, S. & Zielinska, B. 1996 Global mode behavior of the streamwize velocity in wakes. J. Phys. Paris II 6, 1343–1357.Google Scholar
Wesfreid, J. E., Pomeau, Y., Dubois, M., Normand, C. & Bergé, P. 1978 Critical effects In Rayleigh-Benard convection. J. Phys. Paris 39, 725–731.Google Scholar
Williamson, C. H. K. 1988 Defining a universal and continuous Strouhal-Reynolds number relationship for the laminar vortex shedding of a circular cylinder. Phys. Fluids 31, 2742–2744.CrossRefGoogle Scholar
Zielinska, B. J. A., Goujon-Durand, S., Dusek, J. & Wesfreid, J. E. 1997 Strongly nonlinear effect in unstable wakes. Phys. Rev. Lett. 79, 3893–3896.CrossRefGoogle Scholar
Zielinska, B. & Wesfreid, J. E. 1995 On the spatial structure of global modes in wake flow. Phys. Fluids 7, 1418–1424.CrossRefGoogle Scholar
Zippelius, A. & Siggia, E. 1983 Stability of finite amplitude convection. Phys. Fluids 26, 2905–2915.CrossRefGoogle Scholar