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

• Fukumoto, Yasuhide

  Institute of Mathematics for Industry, Kyushu University : Professor

• Mie, Youich

  Sumitomo Rubber Industries Ltd.

Bibliographic Information

Other Title

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

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.

Global COE Program Education-and-Research Hub for Mathematics-for-Industry

Journal

• Fluid dynamics research

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

  IOP Publishing

Keywords

• Fluid Flow and Transfer Processes
• General Physics and Astronomy
• Mechanical Engineering

Details

• CRID: 1050580007682548736
• NII Article ID: 120005690812
• NII Book ID: AA12466655
• DOI: 10.1088/0169-5983/47/1/015509
• ISSN: 18737005
• ISSN: 01695983
• HANDLE: 2324/1434325
• Web Site: https://iopscience.iop.org/article/10.1088/0169-5983/47/1/015509/pdf
• Web Site: https://iopscience.iop.org/article/10.1088/0169-5983/47/1/015509
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN