Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Particulars of the cross- and spanwise near-wake development of a short Semicircular-section Shell, through the TransitionRe-range (60 ≤Re ≤ 600)


Within the fundamental context of quasi-2D bluff-body near-wake investigation, we analyse the way the initial wake vortices (primary and secondary vortices) form and develop with time behind a short (5.2∶1) cylindrical semicircular shell (hollow at the back), after an impulsive start in translation. The study includes the transition regime and non-usual cross-sectional shapes. The structure of the vortices is examined by means of precise visualizations both in the mid-cross and mid-span planes. The particulars induced by the hollow face are deduced from a comparison with the cases of analogous solid cylinders and more particularly with the full semicircular cylinder (Boisaubert et al., 1996; Coutanceau et al., 1998).

The crosswise analysis shows that, except some fundamental difference at the separation initiation and some differences in details, a similar development of the Bénard-Kàrmàn-vortices is observed, thus :

  • - the regime of the occurring structures changes beyond the first phase of development (i.e.t * ≥ 6) when Reynolds number is passing through a critical valueRe c (here 120 ≤Re c ≤ 140)

  • - Kelvin-Helmholtz instabilities are detected forRe = 600 in the rolled-up separated shear layers originating from the sharp body-edges.

On the contrary, the spanwise analysis reveals that the hollow face plays an important role in the time-development of the induced body-end three-dimensionalities (end-vortices and opposite spanwise currents) and intrinsic three-dimensionalities respectively. Thus, as opposed to solid bodies similarly limited in span, the emergence of clear patterns of secondary Taylor-Görtler-like vortices in the near wake have been experimentally proved for the first time whenRe passes beyond the transition value ofRe t ≊ 200. The consequence on the global structure of the flow is deduced.

This is a preview of subscription content, log in to check access.


  1. Abed-Meraïm, K. and Coutanceau, M., Etude de l’écoulement plan engendré par la translation d’une cavité semi-circulaire par visualisation particulaire, In Visualisation et Traitement d’Images en Mécanique des Fluides, (Ed. M. Stanislas and J.C. Monnier, (1990), 278–284., Institut de Mécanique des Fluides de Lille.

  2. Abed-Meraïm, K., Etude expérimentale de l’écoulement plan engendré parla translation d’une coque semi-circulaire pour des nombres de Reynolds allant de 0 à 40, Thèse de l’Université de Poitiers, France (1992).

  3. Albarède, P. and Provansal, M., Quasi-periodic cylinder wakes and the Ginzburg-Landau model, J. Fluid Mech., 291 (1995), 191–222.

  4. Barkley, D. and Henderson, R. D., Three-dimensional Floquet stability analysis of the wake of a circular cylinder, J. Fluid Mech., 322 (1996), 215–241.

  5. Bigeault, K., Etude expérimentale de l’influence de l’inclinaison des plaques de maintien d’un cylindre semi-circulaire sur le développement de son sillage, D. E. A. Université de Poitiers (1998).

  6. Boisaubert, N., Coutanceau, M. and Ehrmann, P., Comparative early development of wake vortices behind a short semicircular-section cylinder in two opposite arrangements, J. Fluid Mech., 327 (1996), 73–99.

  7. Chyu, C. and Rockwell, D., Evolution of patterns of streamwise vorticity in the turbulent near wake of a circular cylinder, J. Fluid Mech., 320 (1996), 117–137.

  8. Coutanceau, M. and Defaye, J. R., Circular cylinder wake configurations: a flow visualization survey, Appl. Mech. Rev., 44 (1991), 255–305.

  9. Coutanceau, M. and Ehrmann, P., Setting up of three-dimensional endplate effect on the starting wake of a perpendicular flat plate, J. of Visualization, 1, 1 (1998), 4.

  10. Coutanceau, M. and Pineau, G., Some typical mechanisms in the early phase of the vortex-shedding process from particle-streak visualization, Atlas of Visualization, Ed. The Visualization Society of Japan, (1997), 43–68, CRC Press.

  11. Coutanceau, M., Ehrmann, P. and Boisaubert, N., Some new insights on the onset and development of three-dimensional end effects and secondary instability in the wake of quasi-2D obstacles, CD ROM Proceedings of the 8th International Symposium on Flow Visualization, Ed. G. M. Carlomagno and I. Grant, (1998).

  12. Coutanceau, M., Migeon, C., Pineau, G. and Texier, A., Starting flow inside a rectangular-section cavity as function of Reynolds number, Proceedings of the fourth Asian Symposium on Visualization, Ed. Q.D. Wei, (1996),65–68, International Academic Publishers.

  13. Ehrmann, P., Etude comparative de la formation des sillages en fonction de la forme des obstacles, Application à la coque semi-circulaire, Thèse de l’Université de Poitiers, France (1996).

  14. Green, R. B. and Gerrard, J. H., Vorticity measurements in the near wake of a circular cylinder at low Reynolds numbers, J. Fluid Mech., 246 (1993), 675–691.

  15. Hasimoto, H., Creeping viscous flow past a circular arc with special reference to separation, J. Phys. Soc. Japan, 47 (1979), 347–348.

  16. Karniadakis, G. E. and Triantafyllou, G. S., Three-dimensional dynamics and transition to turbulence in the wake of bluff bodies, J. Fluid Mech., 238 (1992), 1–30.

  17. Leweke, T. and Provansal, M., The flow behind rings: bluff body wakes without end effects, J. Fluid Mech., 288 (1995), 265–310.

  18. Mansy, H., Yang, P. M. and Williams, D. R., Quantitative measurements of three-dimensional structures in the wake of a circular cylinder, J. Fluid Mech., 270 (1994), 277–296.

  19. Massons, J., Gavalda, Jna., Ruiz, X. and Diaz, F., Image analysis of the wake generated by a Savonius rotor, Wind Eng., 12, 6 (1988), 341–351.

  20. Migeon, C., Etude comparative de la structure des écoulements primaire et secondaires s’établissant dans différents types de cavités cylindriques, Thèse de l’Université de Poitiers, France, (to appear 2000).

  21. Migeon, C., Pineau, G., Coutanceau, M. and Gad el Hak, M., Early time-development of lid-driven cavity flows, Flow Visualization, Ed. J. Crowder.(1995), 54–58 Begell House, Inc.

  22. Noack, B. R. and Eckelmann, H., A global stability analysis of the steady and periodic cylinder wake, J. Fluid Mech., 270 (1994), 297–330.

  23. Noack, B. R., König, M. and Eckelmann, H., Three-dimensional stability analysis of the periodic flow around a circular cylinder, Phys Fluids A 5 (1993), 1279–1281.

  24. Pineau, G., Mise en évidence et évaluation des effets tridimensionnels dans l’écoulement instationnaire autour d’un cylindre circulaire d’envergure finie, Thèse de l’Université de Poitiers, France (1992).

  25. Pineau, G., Texier, A., Coutanceau, M. and Ta Phuoc Loc, Experimental and numerical visualization of the 3D-flow around a short circular cylinder fitted with end-plates, In Flow Visualization, Ed. Y. Tanida and H. Miyashiro, (1992), 343–347, Springer Verlag.

  26. Polidori, G., Etude par visualisation de sillages tridimensionnels, Application à un profil d’aile rectangulaire, Thèse de l’Université de Poitiers, France (1994).

  27. Polidori, G., Pineau, G., Abed Meraïm, K. and Coutanceau, M., Shedding Process of the Initial Vortices from Impulsively Started Cylinders at Re = 1000; End and Body Geometry Effects, In Bluff-Body wakes, Dynamics and Instabilities, Ed. H. Eckelmann, J.M.R. Graham, P. Huerre and P.A. Monkewitz, (1992), 285–288, Springer Verlag.

  28. Prasad, A. and Williamson, C. H. K., The instability of the shear layer separating from a bluff body, J. Fluid Mech., 333 (1997), 375–402.

  29. Rosko, A., On the development of turbulent wakes from vortex streets, NACA Rep., 1191 (1954), 1–25.

  30. Taneda, S., Visualization of separating Stokes flows, J. Phys. Soc. Japan, 46 (1979), 1935–1942.

  31. Tomboulides, A. G., Triantafyllou, G. S. and Karniadakis, G. E., A new mechanism of period doubling in free shear flows, Phys. Fluids A4 (1992), 1329–1332.

  32. Tritton, D. J., Experiments on the flow past a circular cylinder at low Reynolds numbers, J. Fluid Mech., 6 (1959), 547–567.

  33. Williamson, C. H. K., Three-dimensional wake transition, J. Fluid Mech., 328 (1996a), 345–407.

  34. Williamson, C. H. K. Vortex dynamics in the cylinder wake, Ann. Rev. Fluid Mech., 28 (1996b), 477–539.

  35. Wu, J., Sheridan, J., Welsch, M. C. and Hourigan, K., Three-dimensional vortex structures in a cylinder wake, J. Fluid Mech., 312 (1996), 201–222.

  36. Zhang, H. Q., Fey, U., Noack, B. R., König, M. and Eckelmann, H., On the transition of the cylinder wake, Phys. Fluids, 7 (4) (1995), 779–794.

  37. Zhang, H. Q., Noack, B. R. and Eckelmann, H., Numerical computation of the 3-D cylinder wake, Report No 3/1994, Max-Planck-Institut für Strömungsforschung, Göttingen (1994).

Download references

Author information

Correspondence to M. Coutanceau.

Additional information

Author Profile Madeleine Coutanceau: She was (up to 1995) Professor of Fluid Mechanics at the University of Poitiers, France, from which she received her Doctorat ès Sciences in 1971. She was at the head of a research group working mainly in the domain of flow visualization. Her main themes of research include the investigation of viscous flows around obstacles with rigid or free surfaces, such as drops and bubbles, in Newtonian and non-Newtonian liquids, and the time development of wakes around bluff bodies and aerodynamic profiles subjected to various motions after an impulsive start. She is currently an Honorary Professor of the University of Poitiers, a member of the Association Universitaire de Mécanique, of the Scientific Committee of the Colloque National de Visualisation et de Traitement d’Images en Mécanique des Fluides and of the International Organizing Board of the International Symposium on Flow Visualization.

Christophe Migeon: He received his master degree from the University of Poitiers, France, in 1995. He is currently about to get his Ph.D. in Aerodynamics and Fluid Mechanics from the same University. His theme of research is related to the two- and three-dimensional study of various lid-driven cavity-flows. At the same time, he is a lecturer at the Institut National de Sciences Appliquées (INSA) in Rennes, France.

Patrick Erhmann: He received his master degree (1992) and his Ph.D. (1996) from the University of Poitiers, France, in the domain of Aerodynamics and Fluid Mechanics. His theme of research was related to the comparative study of wake formation as function of the body shape. He is currently a manager in the french automotive branch of a US firm.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Coutanceau, M., Migeon, C. & Ehrmann, P. Particulars of the cross- and spanwise near-wake development of a short Semicircular-section Shell, through the TransitionRe-range (60 ≤Re ≤ 600). J Vis 3, 9–26 (2000).

Download citation


  • three-dimensional formation
  • cylindrical shell
  • cross and spanwise visualization
  • primary and secondary instabilities