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Primary and secondary instabilities of the asymptotic suction boundary layer on a curved plate

Published online by Cambridge University Press:  26 April 2006

Daniel S. Park  and
Patrick Huerre
Daniel S. Park
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA Present address: Naval Command, Control and Ocean Surveillance Center, RDT&E Division, Code 574, San Diego, CA 92152-6040, USA.
Patrick Huerre
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA Present address: Laboratoire d'Hydrodynamique (LADHYX), Ecole Polytechnique, 91128 Palaiseau Cedex, France.
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Abstract

The temporal growth of Görtler vortices and the associated secondary instability mechanisms are investigated numerically in the case of an asymptotic suction boundary layer on a curved plate. Highly inflectional velocity profiles are generated in both the spanwise and vertical directions. The inflectional velocity profile develops earlier in the spanwise direction. There exist two distinct modes of instability that eventually lead to the breakdown of Görtler vortices: the sinuous mode and the varicose mode. The temporal secondary instability analysis of the three-dimensional inflectional velocity profile reveals that the sinuous mode becomes unstable earlier than the varicose mode. The sinuous mode is shown to be primarily related to shear in the spanwise direction, ∂U/∂z, and the varicose mode to shear in the vertical direction, ∂U/∂y.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 283 , 25 January 1995 , pp. 249 - 272
Copyright
© 1995 Cambridge University Press

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References

Aihara, Y. 1979 Görtler vortices in the nonlinear region. In Recent Developments in Theoretical and Experimental Fluid Mechanics, pp. 331–338. Springer.
Aihara, Y. & Koyama, H. 1981 Secondary instability of Görtler vortices – formation of periodic three-dimensional coherent structure. Trans. Japan Soc. Aero. Astron. Sci. 24, 78–94.Google Scholar
Aihara, Y. & Sonoda, T. 1981 Effects of pressure gradient on the secondary instability of Görtler vortices. AIAA-81-0191.
Alfredsson, P. H. & Matsson, O. J. E. 1990 The effect of curvature and rotation on the stability of channel flow. In Colloquium on Görtler Vortex Flows, Synopsis of Contributions. EUROMECH 261, Université de Nante, France.
Bassom, A. P. & Seddougui, S. O. 1990 The onset of three-dimensionality and time dependence on Görtler vortices: neutrally stable wavy modes. J. Fluid Mech. 220, 661–672.Google Scholar
Bippes, H. 1972 Experimente Untersuchung des laminar-turbulenten Umschlags an einer parallel angeströmten könkaven Wand. Heidelberger Akademie der Wiss. Math. Naturw. Klasse, pp. 103–180.
Blackwelder, R. F. & Swearingen, J. D. 1988 The role of inflectional velocity profiles in wall bounded flows. In Near-Wall Turbulence (ed. S. J. Kline). Hemisphere.
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Finley, W. H., Keller, J. B. & Ferziger, J. H. 1988 Instability and transition in curved channel flow. J. Fluid Mech. 194, 417–456.Google Scholar
Floryan, J. M. & Saric, W. S. 1979 Stability of Görtler vortices in boundary layers. AIAA J. 20, 316–324.Google Scholar
Göurtler, H. 1940 Über eine dreidimensionale Instabilität laminarer Grenzschichten an konkaven Wänden. Nachr. Ges. Wiss. Göttingen, Math. Phys. Klasse, Neue Folge 2, 1–26.Google Scholar
Hall, P. 1982a On the nonlinear evolution of Görtler vortices in growing boundary layers. J. Inst. Maths Applics. 29, 173–196.Google Scholar
Hall, P. 1982b Taylor-Görtler instabilities in fully developed or boundary layer flows: linear theory. J. Fluid Mech. 124, 475–494.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. 1988 The nonlinear development of Görtler vortices in growing boundary layers. J. Fluid Mech. 193, 243–266.Google Scholar
Hall, P. & Horseman, N. J. 1991 The linear inviscid secondary instability of longitudinal vortex structures in boundary layers. J. Fluid Mech. 232, 357–375.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. O. 1989 On the onset of three-dimensionality and time-dependence in Görtler vortices. J. Fluid Mech. 204, 405–420.Google Scholar
Hall, P. & Smith, F. T. 1991 On strongly nonlinear vortex/wave interactions in boundary-layer transition. J. Fluid Mech. 227, 641–666.Google Scholar
Ho, C. M. & Huerre, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365–424.Google Scholar
Ito, A. 1980 The generation and breakdown of longitudinal vortices along a concave wall. J. Japan Soc. Aerospace Sci. 28, 327–333.Google Scholar
Ito, A. 1988 On the relation of horseshoe-type vortices and fluctuating flows. J. Japan Soc. Aerospace Sci. 36, 274–279.Google Scholar
Liu, W. 1991 Direct numerical simulation of transition to turbulence in Görtler flow PhD Thesis, University of Southern California, Department of Aerospace Engineering.
Liu, W. & Domaradzki, J. A. 1990 Direct numerical simulation of transition to turbulence in Görtler flow. AIAA-90-0114.
Myose, R. Y. & Blackwelder, R. F. 1991 Controlling the spacing of streamwise vortices on concave walls. AIAA J. 20, 1901–1905.Google Scholar
Park, D. S. 1990 The primary and secondary instabilities of Görtler flow PhD Thesis, University of Southern California, Department of Aerospace Engineering.
Park, D. S. & Huerre, P. 1990 The secondary instability of the nonlinearly developing Görtler vortices. In Colloquium on Görtler Vortex Flows, Synopsis of Contributions. EU-ROMECH 261, Université de Nantes, France.
Peerhossaini, H. 1984 On the subject of Görtler vortex. In Cellular Structures in Instabilities (ed. J. E. Wesfreid & S. Zaleski), pp. 376–384. Springer.
Peerhossaini, H. & Wesfreid, J. E. 1988 On the inner structure of streamwise Görtler rolls. Intl J. Heat Fluid Flow 9, 12–18.Google Scholar
Rayleigh, Lord 1916 On the dynamics of revolving fluids. Proc. R. Soc. Lond. A 93, 148–154.Google Scholar
Sabry, A. S. & Liu, J. T. C. 1991 Longitudinal vorticity elements in boundary layers: nonlinear development from initial Görtler vortices as a prototype problem. J. Fluid Mech. 231, 615–663.Google Scholar
Smith, C. R., Walker, J. D. A., Haidari, A. H. & Sobrun, U. 1991 On the dynamics of near-wall turbulence. Phil. Trans. R. Soc. Lond. A 336, 131–175.Google Scholar
Swearingen, J. D. & Blackwelder, R. F. 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 255–290.Google Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289–343.Google Scholar
Winoto, S. H. & Crane, R. I. 1980 Vortex structure in laminar boundary layers on a concave wall. Intl J. Heat Fluid Flow 2, 221–231.Google Scholar