The Effect of Nonlinearity and Forcing on Global Modes

  • J. M. Chomaz
  • P. Huerre
  • L. G. Redekopp
Part of the NATO ASI Series book series (NSSB, volume 237)


Representation of the linear disturbance field in terms of local modes is firmly established for wave guides where the propagation space is homogeneous.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bers, A., 1975. Linear waves and instabilities. Physique de Plasmas, eds. C. DeWitt and J. Peyraud, pp. 117–215. Gordon and Breach, New York.Google Scholar
  2. 2.
    Bers, A., 1983. Space-time evolution of plasma instabilities-absolute and convective. Handbook of Plasma Physics, eds. M.N. Rosenbluth and R.Z. Sagdeev, pp. 1: 451–517. North-Holland, Amsterdam.Google Scholar
  3. 3.
    Briggs, R. J., 1964. Electron-Stream Interaction with Plasmas. MIT Press, Cambridge.Google Scholar
  4. 4.
    Chomaz, J. M., Huerre, P., and Redekopp, L. G., 1987. Models of hydrodynamic resonances in separated shear flows. Proc. 6th Symp. Turb. Shear Flows, pp. 3. 2. 1–6.Google Scholar
  5. 5.
    Chomaz, J. M., Huerre, P., and Redekopp, L. G., 1988. Bifurcations to local and global modes in spatially-developing flows. Phys. Rev. Lett., 60: 25–28.CrossRefGoogle Scholar
  6. 6.
    Chomaz, J. M., Huerre, P., and Redekopp, L. G., 1989. A frequency selection criterion in spatially-developing flows. Stud. Appl. Math., (submitted for publication).Google Scholar
  7. 7.
    Deissler, R. J., 1985. Noise-sustained structure, intermittency, and the Ginzburg-Landau equation. J. Stat. Phys., 40: 371–95MathSciNetCrossRefGoogle Scholar
  8. 8.
    Deissler, R. J., 1987. Spatially-growing waves, intermittency and convective chaos in an open-flow system. Physica D, 25: 233–260CrossRefGoogle Scholar
  9. 9.
    Hannemann, K., and Oertel, Jr. H., 1988. Numerical simulation of the absolutely and convectively unstable wake. J. Fluid Mech., 199: 55–88.CrossRefGoogle Scholar
  10. 10.
    Huerre, P., and Monkewitz, P. A., 1990. Local and global instabilities in spatially-developing flows. Ann. Rev. Fluid Mech.,Vol. 22 (in press).MathSciNetCrossRefGoogle Scholar
  11. 11.
    Jackson, C. P., 1987. A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech., 182: 23–45.CrossRefGoogle Scholar
  12. 12.
    Lifshitz, E. M., and Pitaevskii, L. P., 1981. Physical Kinetics. Chapter V I. Pergamon, London.Google Scholar
  13. 13.
    Mathis, C., Provansal, M., and Boyer, L., 1984. The Bénard-von Karman instability: an experimental study near the threshold. J. Phys. Lett. (Paris), 45: 483–491.CrossRefGoogle Scholar
  14. 14.
    Monkewitz, P. A., 1988. The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers. Phys. Fluids, 31: 999–1006.CrossRefGoogle Scholar
  15. 15.
    Newell, A. C., 1974. Envelope equations. Lect. Appl. Math., ed A.C. Newell, Vol. 15, pp. 157–163. Ara. Math. Soc., Providence, RI.Google Scholar
  16. 16.
    Provansal, M., Mathis, C., and Boyer, L., 1987. Bénard-von Karman instability: transient and forced regimes. J. Fluid Mech., 182: 1–22.CrossRefGoogle Scholar
  17. 17.
    Sreenivasan, K. R., Strykowski, P. J., and Olinger, D. J., 1987. Hopf bifurcation, Landaw equation and vortex shedding behind circular cylinders. Proc. Forum on Unsteady Flow Separation, ed. K. N. Ghia. ASME FED. Vol. 52.Google Scholar
  18. 18.
    Sreenivasan, K. R., Strykowski, P. J., and Olinger, D. J., 1989. On the Hopf bifurcation and Landau-Stuart constants associated with vortex ‘shedding’ behind circular cylinders. J. Fluid Mech., (submitted for publication).Google Scholar
  19. 19.
    Sturrock, P. A., 1961. Amplifying and evanescent waves, convective and non-convective instabilities. Plasma Physics, ed. J.E. Drummond, pp. 124–42. McGraw-Hill, New York.Google Scholar
  20. 20.
    Yang, X. and Zebib, A., 1989. Absolute and convective instability of a cylinder wake. Phys. Fluids, Al: 689–696.Google Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • J. M. Chomaz
    • 1
  • P. Huerre
    • 2
  • L. G. Redekopp
    • 2
  1. 1.Meteorologie Nationale CNRMToulouse CedexFrance
  2. 2.Department of Aerospace EngineeringUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations