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Landau Equation and Multiple Hopf-Bifurcation

  • Tapan K. Sengupta
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 517)

Abstract

The linear theory of stability of a steady basic flow generally gives a spectrum of independent modes with velocity perturbation of the form,
$$ u'(\overrightarrow X ,t) = \sum\limits_{j = 1}^\infty {Aj(t)fj} (\overrightarrow X ) + A_j^* (t)f_j^* (\overrightarrow X ) $$
(5.1.1)
where the quantities with asterisks denote complex conjugate. In the linear stability theory we generally focus upon one mode at a time- the so-called normal mode analysis. If the complex amplitude of any one of the mode that grows with time is given by
$$ Aj(t) = Const.e^{s_j t} $$
(5.1.2)
then it is easy to see that the evolution equation for the amplitude of this mode is given by,
$$ \frac{{dAj}} {{dt}} = sjAj $$
(5.1.3)

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Copyright information

© CISM, Udine 2010

Authors and Affiliations

  • Tapan K. Sengupta
    • 1
  1. 1.HPCL, Aerospace EngineeringI.I.T. KanpurKanpur

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