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

Yasuhide Fukumoto, Youichi Mie

Research output: Contribution to journalArticle


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.

Original languageEnglish
Article number015509
Pages (from-to)1-14
Number of pages14
JournalFluid Dynamics Research
Issue number1
Publication statusPublished - Feb 1 2015


All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Fluid Flow and Transfer Processes

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