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Article
Floquet analysis of secondary instability of boundary layers distorted by Klebanoff streaks and Tollmien-Schlichting waves
Physics of Fluids
  • Yang Liu, Stanford University
  • Tamer A. Zaki, Imperial College London
  • Paul A. Durbin, Iowa State University
Document Type
Article
Publication Version
Published Version
Publication Date
1-1-2008
DOI
10.1063/1.3040302
Abstract

Previous studies of the interaction between boundary layer streaks and Tollmien-Schlichting (TS) waves have shown puzzling effects. Streaks were shown to reduce the growth rate of primary TS waves and, thereby, to delay transition; however, they can also promote transition by inducing a secondary instability. The outcome of the interaction depends on the spanwise wavelength and intensity of the streaks as well as on the amplitude of the TS waves. A Floquet analysis of secondary instability is able to explain many of these features. The base state is periodic in two directions: it is an Ansatz composed of a saturated TS wave (periodic in x) and steady streaks (periodic in z). Secondary instability analysis is extended to account for the doubly periodic base flow. Growth rate computations show that, indeed, the streak can either enhance or diminish the overall stability of the boundary layer. The stabilizing effect is a reduction in the growth rate of the primary two-dimensional TS wave; the destabilizing effect is a secondary instability. Secondary instability falls into two categories, depending on the spanwise spacing of the streaks. The response of one category to perturbations is dominated by fundamental and subharmonic instability; the response of the other is a detuned instability.

Comments

The following article appeared in Physics of Fluids 20, 124102 (2008); and may be found at doi: 10.1063/1.3040302.

Rights
Copyright 2008 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
Copyright Owner
American Institute of Physics
Language
en
Date Available
2015-08-26
File Format
application/pdf
Citation Information
Yang Liu, Tamer A. Zaki and Paul A. Durbin. "Floquet analysis of secondary instability of boundary layers distorted by Klebanoff streaks and Tollmien-Schlichting waves" Physics of Fluids Vol. 20 Iss. 12 (2008) p. article no. 124102
Available at: http://works.bepress.com/paul_durbin/8/