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On the Absolute/Convective Nature of Primary and Secondary Instabilities

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Propagation in Systems Far from Equilibrium

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 41))

Abstract

Primary and secondary instabilities arising in fluid flows need not have the same absolute/convective character. The Newell-Whitehead-Segel evolution model is chosen to illustrate this phenomenon. It is shown that the Eckhaus instability can be either absolute or convective in a parameter domain of absolute primary instability. In the case of the cubic Nonlinear Schrodinger Equation, the Benjamin-Feir instability is determined to be absolute as soon as the amplitude of the Stokes wavetrain exceeds a certain threshold. These two problems also provide simple examples of application of the absolute/convective instability criterion.

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Authors and Affiliations

  1. Department of Aerospace Engineering, University of Southern California, Los Angeles, CA, 90089, USA

    P. Huerre

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  1. P. Huerre
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Editor information

Editors and Affiliations

  1. Laboratoire d’Hydrodynamique et Mécanique Physique, E.S.P.C.I. Paris, 10, rue Vauquelin, F-75231, Paris Cedex 05, France

    José E. Wesfreid

  2. Fachbereich 7 (Physik), Universität Essen, D-4300, Essen 1, Fed. Rep. of Germany

    Helmut R. Brand

  3. IRF-DPh-G/PSRM, CEN-Saclay, F-91191, Gif-sur-Yvette, France

    Paul Manneville

  4. Lab. de Recherches en Combustion, Université de Provence, Centre St. Jérôme, F-13397, Marseille Cedex 13, France

    Gilbert Albinet

  5. Centre de Physique Théorique, F-74310, Les Houches, France

    Nino Boccara

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© 1988 Springer-Verlag Berlin Heidelberg

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Huerre, P. (1988). On the Absolute/Convective Nature of Primary and Secondary Instabilities. In: Wesfreid, J.E., Brand, H.R., Manneville, P., Albinet, G., Boccara, N. (eds) Propagation in Systems Far from Equilibrium. Springer Series in Synergetics, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73861-6_33

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  • DOI: https://doi.org/10.1007/978-3-642-73861-6_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-73863-0

  • Online ISBN: 978-3-642-73861-6

  • eBook Packages: Springer Book Archive

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