Skip to main content

The Modelling of the Wake of a Torus by the Ginzburg-Landau Equation

  • Chapter
Computation of Three-Dimensional Complex Flows

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NONUFM,volume 49))

  • 268 Accesses

Summary

The wake of a torus is studied in the Reynolds number range [50, 300]. In the periodic regime different modes of vortex shedding, parallel closed rings or oblique helical lines of vortices, have been observed. We present their limits of stability as functions of the control parameter. At higher Reynolds number a chaotic regime of vortex shedding is characterized by a discontinuity in the velocity-frequency relation. Both these regimes are well described by the GinzburgLandau equation which allows to interprete many phenomena as consequences of the Eckaus or Benjamin-Feir instabilities.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Albarède and P. A. Monkewitz, Phys. Fluids A 4, 744 (1992).

    Article  Google Scholar 

  2. T. Leweke, M. Provansal, and L. Boyer, C. R. Acad. Sci. Paris 316, Série II, 287 (1993).

    Google Scholar 

  3. T. Leweke, M. Provansal, and L. Boyer, Phys. Rev. Lett. 71, 3469 (1993).

    Article  Google Scholar 

  4. P. Albarède and M. Provansal, J. Fluid Mech. vol 291, 191–222. (1995).

    Google Scholar 

  5. M. S. Bloor, J. Fluid Mech. 19, 290 (1964).

    Article  MATH  Google Scholar 

  6. C. H. K. Williamson, J. Fluid Mech. 206, 579 (1989).

    Article  Google Scholar 

  7. M. König, H. Eisenlohr, and H. Eckelmann, Phys. Fluid A 2, 1607 (1990).

    Article  Google Scholar 

  8. M. Hammache and M. Gharib, J. Fluid Mech. 232, 567 (1991).

    Article  Google Scholar 

  9. T. Leweke and M. Provansal, J. Fluid Mech vol 288, 265–310. (1995).

    Article  Google Scholar 

  10. C. H. K. Williamson, Phys. Fluids 31, 3165 (1988).

    Article  Google Scholar 

  11. M. Provansal, C. Mathis, and L. Boyer, J. Fluid Mech. 182, 1 (1987).

    Article  MATH  Google Scholar 

  12. L. D. Landau, C. R. Acad. Sci. URSS 44, 311 (1944).

    MATH  Google Scholar 

  13. K. R. Sreenivasan, P. J. Strykowski, and D. J. Ohlinger, in Forum on Unsteady Flow Separation, edited by K. N. Ghia (ASME, New York, 1986), FED-Vol. 52, pp. 1–13.

    Google Scholar 

  14. M. Schumm, E. Berger, and P. A. Monkewitz, submitted to J. Fluid Mech. (1994).

    Google Scholar 

  15. T. Leweke and M. Provansal, Eur. Phys. Lett. 27, 655(1994).

    Article  Google Scholar 

  16. B. I. Shraiman, A. Pumir, W. van Saarlos, P. C. Hohenberg, H. Chaté and M. Holen, Physica (Amsterdam) 57D, 241 (1992).

    Google Scholar 

  17. D. Barckley and R.D. Henderson Three-dimensional Hoquet stability analysis of the wake of a circular cylinder. Submitted to J. Huid Mech. (1995).

    Google Scholar 

  18. H. Zhang, U. Pey, B.R. Noack, M. König and H. Eckelmann Phys. Fluids. 7, 779 (1995).

    Article  Google Scholar 

  19. C. Dauchy, J. Dusek and P. Fraunié 12ème Congrès de Mécanique, Strasbourg (1995).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Michel Deville Spyros Gavrilakis Inge L. Ryhming

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden

About this chapter

Cite this chapter

Provansal, M., Leweke, T. (1996). The Modelling of the Wake of a Torus by the Ginzburg-Landau Equation. In: Deville, M., Gavrilakis, S., Ryhming, I.L. (eds) Computation of Three-Dimensional Complex Flows. Notes on Numerical Fluid Mechanics (NNFM), vol 49. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89838-8_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-322-89838-8_31

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-322-89840-1

  • Online ISBN: 978-3-322-89838-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics