Lagrangian approach to weakly nonlinear interaction of Kelvin waves and a symmetry-breaking bifurcation of a rotating flow

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Abstract

We develop a general framework of using the Lagrangian variables for calculating the energy of waves on a steady Euler flow and the mean flow induced by their nonlinear interaction. With the mean flow at hand we can determine, without ambiguity, all the coefficients of the amplitude equations to third order in amplitude for a rotating flow subject to a steady perturbation breaking the circular symmetry of the streamlines. Moreover, a resonant triad of waves is identified which brings in the secondary instability of the Moore–Saffman–Tsai–Widnall instability, and with the aid of the energetic viewpoint, resonant amplification of the waves without bound is numerically confirmed.

Journal

  • Fluid dynamics research

    Fluid dynamics research 47(1), 015509, 2015-02

    IOP Publishing

Codes

  • NII Article ID (NAID)
    120005690812
  • NII NACSIS-CAT ID (NCID)
    AA12466655
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    1873-7005
  • Data Source
    IR 
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