On the Absolute/Convective Nature of Primary and Secondary Instabilities

  • P. Huerre
Part of the Springer Series in Synergetics book series (SSSYN, volume 41)


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.


Saddle Point Secondary Instability Unstable Case Nonlinear Schrodinger Equation Unstable Flow 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • P. Huerre
    • 1
  1. 1.Department of Aerospace EngineeringUniversity of Southern CaliforniaLos AngelesUSA

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