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Taylor—Gortler vortices in fully developed or boundary-layer flows: linear theory

Published online by Cambridge University Press:  20 April 2006

P. Hall
P. Hall
Affiliation:
Department of Mathematics, Imperial College, London
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Abstract

The stability characteristics of some fluid flows at high Taylor or Gortler numbers are determined using perturbation methods. In particular, the stability characteristics of some fully developed flows between concentric cylinders driven either by a pressure gradient or the motion of the inner cylinder are investigated. The asymptotic structure of short-wavelength disturbances to these flows is obtained and used as a basis for a formal perturbation solution to the corresponding stability problem appropriate to a developing boundary layer. The non-parallel effect of the basic flow on the condition for neutral stability is discussed. The results obtained suggest that the disturbances are concentrated in internal viscous or critical layers well away from the wall and the free stream. The stability of a boundary layer on a concave wall to Görtler vortices that propagate downstream is also considered. These modes are found to be more stable than the usual time-independent modes and they propagate downstream with the speed of the basic flow in the critical layer. Some comparison with previous experimental and theoretical work is given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 124 , November 1982 , pp. 475 - 494
Copyright
© 1982 Cambridge University Press

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References

Bippes, H. & Görtler, H. 1972 Acta Mech. 14, 251.
Chandrasekhar, S. 1958 Hydrodynamic and Hydromagnetic Stability. Clarendon.
Davey, A., DiPrima, R. C. & Stuart, J. T. 1969 J. Fluid Mech. 31, 17.
Dean, W. R. 1928 Proc. R. Soc. Lond. A 121, 402.
Floryan, J. & Saric, W. 1979 A.I.A.A. Paper no. 79–1497.
Gaster, M. 1974 J. Fluid Mech. 64, 465.
Görtler, H. 1940 NACA Tech. Memo. no. 1357.
Gregory, N. & Walker, W. S. 1950 A.R.C. R. & M. no. 2779.
Hämmerlin, G. 1955 J. Rat. Mech. Anal. 4, 279.
Hämmerlin, G. 1956 Z. angew. Math. Phys. 7, 156.
Herbert, T. 1976 Arch. Mech. 28, 1039.
Meksyn, D. 1946 Proc. R. Soc. Lond. A 187, 115.
Smith, A. M. O. 1955 Appl. Math. 13, 233.
Smith, F. T. 1979 Proc. R. Soc. Lond. A 366, 91.
Smith, F. T. 1980 Proc. R. Soc. Lond. A 368, 573.
Stuart, J. T. 1963 In Laminar Boundary Layers (ed. L. Rosenhead), chap. X. Oxford University Press.
Tani, I. & Sakagami 1962 J. Proc. Int. Council Aero. Sci. Third Congress, p. 391.
Taylor, G. I. 1923 Phil. Trans. R. Soc. Lond. A 223, 289.