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The onset of three-dimensionality and time-dependence in Görtler vortices: neutrally stable wavy modes

Published online by Cambridge University Press:  26 April 2006

Andrew P. Bassom  and
Sharon O. Seddougui
Andrew P. Bassom
Affiliation:
Department of Mathematics, North Park Road, University of Exeter, Exeter, EX4 4QE, UK
Sharon O. Seddougui
Affiliation:
Institute of Computer Applications in Science & Engineering, NASA Langley Research Centre, Hampton, VA 23665, USA
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Abstract

Recently Hall & Seddougui (1989) considered the secondary instability of large-amplitude Görtler vortices in a growing boundary layer into a three-dimensional flow with wavy vortex boundaries. They obtained a pair of coupled, linear ordinary differential equations for this instability which constituted an eigenproblem for the wavelength and frequency of this wavy mode. In the course of investigating the nonlinear version of this problem (Seddougui & Bassom 1990), we have found that the numerical work of Hall & Seddougui (1989) is incomplete; this deficiency is rectified here. In particular, we find that many neutrally stable modes are possible; we derive the properties of such modes in a high-wavenumber limit and show that the combination of the results of Hall & Seddougui and our modifications lead to conclusions which are consistent with the available experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 220 , November 1990 , pp. 661 - 672
Copyright
© 1990 Cambridge University Press

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References

Aihara, Y. & Koyama, H., 1981 Secondary instability of Görtler vortices: formation of periodic three-dimensional coherent structures. Trans. Japan Soc. Aero. Space Sci. 24, 78–94.Google Scholar
Bippes, H. & Görtler, H. 1972 Dreidimensionales Störungen in der Grenzschicht an einer Konkaven Wand. Acta. Mech. 14, 251–267.Google Scholar
Hall, P.: 1982a Taylor–Görtler vortices in fully developed or boundary layer flows: linear theory. J. Fluid Mech. 124, 475–494.Google Scholar
Hall, P.: 1982b On the nonlinear evolution of Görtler vortices in non-parallel boundary layers. IMA J. Appl. Maths 29, 173–196.Google Scholar
Hall, P.: 1983 The linear development of Görtler vortices in growing boundary layers. J. Fluid Mech. 130, 41–58.Google Scholar
Hall, P. & Lakin, W. D., 1988 The fully nonlinear development of Görtler vortices in growing boundary layers. Proc. R. Soc. Lond. A 415, 421–444.Google Scholar
Hall, P. & Seddougui, S., 1989 On the onset of three-dimensionality and time-dependence in Görtler vortices. J. Fluid Mech. 204, 405–420 (referred to herein as HS).Google Scholar
Hastings, S. P. & Mcleod, J. B., 1980 A boundary value problem associated with the Second Painlevé Transcendent and the Korteweg–de Vries equation. Arch. Rat. Mech. Anal. 73, 31–51.Google Scholar
Kohama, Y.: 1988 Three-dimensional boundary layer transition on a convex–concave wall. In Proc. Bangalore IUTAM Symp. on Turbulence Managamenent and Relaminarisation (ed. H. Liepmann & R. Narasimha), pp. 215–226. Springer.
Peerhossaini, H. & Wesfreid, J. E., 1988a On the inner structure of streamwise Görtler rolls. Intl J. Heat Fluid Flow 9, 12–18.Google Scholar
Peerhossaini, H. & Wesfreid, J. E., 1988b Experimental study of the Taylor–Görtler instability. In Propagation in Systems Far from Equilibrium (ed. J. E. Wesfreid, H. R. Brand, P. Manneville, G. Albinet & N. Boccara). Springer Series in Synergetics, vol. 41, pp. 399–412. Springer.
Seddougui, S. O. & Bassom, A. P., 1990 On the instability of Görtler vortices to nonlinear travelling waves. ICASE Rep. 90–1 (IMA J. Appl. Maths, to appear).Google Scholar