Floquet analysis of fundamental, subharmonic and detuned secondary instabilities of Görtler vortices

Jie Ren, Song Fu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

Nonlinear parabolized stability equations are employed in this work to investigate the nonlinear development of the Görtler instability up to the saturation stage. The perturbed boundary layer is highly inflectional both in the normalwise and spanwise directions and receptive to the secondary instabilities. The Floquet theory is applied to solve the fundamental, subharmonic and detuned secondary instabilities. With the Görtler-vortices- distorted base flow, two classes of secondary disturbances, i.e. odd modes and even modes, are identified according to the eigenfunctions of the disturbances. These modes may result in different patterns in the late stages of the transition process. Li and Malik [1] have shown the sinuous and varicose types of breakdown originating from the odd and even modes. The current study focuses on the four most amplified modes termed the even modes I & II and odd modes I & II. Odd mode II was missing in the work of Li and Malik [1] probably due to their inviscid simplification. The detuned modes are confirmed to be less amplified than the fundamental (for the odd mode I) and subharmonic modes (for even modes I & II and the odd mode II).

Original languageEnglish
Pages (from-to)555-561
Number of pages7
JournalScience China: Physics, Mechanics and Astronomy
Volume57
Issue number3
DOIs
Publication statusPublished - Mar 2014
Externally publishedYes

Keywords

  • Floquet theory
  • Görtler vortices
  • secondary instability

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