Evolution of an elliptical flow in weakly nonlinear regime

Yuji Hattori, Yasuhide Fukumoto, Kaoru Fujimura

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the nonlinear evolution of an elliptical flow by weakly nonlinear analysis. Two sets of amplitude equations are derived for different situations. First, the weakly nonlinear evolution of helical modes is considered. Nonlinear selfinteraction of the two base Kelvin waves results in cubic nonlinear terms, which causes saturation of the elliptical instability. Next, the case of triad interaction is considered. Three Kelvin waves, one of which is a helical mode, form a resonant triad thanks to freedom of wavenumber shift. As a result three-wave equations augmented with linear terms are obtained as amplitude equations. They explain the numerical results on the secondary instability obtained by Kerswell (1999).

Original languageEnglish
Title of host publicationIUTAM Symposium on Computational Physics and New Perspectives in Turbulence - Proceedings of the IUTAM Symposium on Computational Physics and New Perspectives in Turbulence
Pages433-438
Number of pages6
DOIs
Publication statusPublished - 2008 Dec 1
Externally publishedYes
EventIUTAM Symposium on Computational Physics and New Perspectives in Turbulence - Nagoya, Japan
Duration: 2006 Sep 112006 Sep 14

Publication series

NameSolid Mechanics and its Applications
Volume4
ISSN (Print)1875-3507

Other

OtherIUTAM Symposium on Computational Physics and New Perspectives in Turbulence
CountryJapan
CityNagoya
Period06/9/1106/9/14

Keywords

  • Amplitude equations
  • Elliptical flow
  • Elliptical instability
  • Secondary instability
  • Weakly nonlinear analysis

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Automotive Engineering
  • Aerospace Engineering
  • Acoustics and Ultrasonics
  • Mechanical Engineering

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  • Cite this

    Hattori, Y., Fukumoto, Y., & Fujimura, K. (2008). Evolution of an elliptical flow in weakly nonlinear regime. In IUTAM Symposium on Computational Physics and New Perspectives in Turbulence - Proceedings of the IUTAM Symposium on Computational Physics and New Perspectives in Turbulence (pp. 433-438). (Solid Mechanics and its Applications; Vol. 4). https://doi.org/10.1007/978-1-4020-6472-2_66