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Linear stability of two-dimensional flow to three-dimensional perturbations in a channel with a flexible wall

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we investigate the effects of three-dimensional disturbance waves on the stability of a two-dimensional channel flow with one compliant surface. The study exploits the multideck structure of the flow in the limit of large Reynolds numbers to make an asymptotic analysis of the flow and to derive linear neutral stability results. The study shows that for a flow over flexible surfaces, three-dimensional disturbances may be more unstable than two-dimensional modes for a given set of wall properties.
Rocznik
Strony
293--311
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • School of Mathematical Sciences University of KwaZulu-Natal, P Bag X01 Scottsville 3209, Pietermaritzburg, RSA
autor
  • Mathematics Department University of Swaziland, P Bag 4, Kwaluseni, Swaziland
autor
  • Department of Mathematics Bindura University, P Bag 1020, Bindura, Zimbabwe
Bibliografia
  • 1. T.B. Benjamin, Effects of a flexible boundary on hydrodynamic stability, J. Fluid Mech., 9, 513–532, 1960.
  • 2. A.P. Bassom and J. S.B. Gajjar, Upper-branch instability of flow in pipes of large aspect ratios with three-dimensional nonlinear viscous critical layers, IMA J. Appl. Math., 42, 119–145, 1989.
  • 3. P. W. Carpenter, The effects of damping on the hydrodynamic stability of flows over Kramer-type compliant surfaces, In laminar/turbulent boundary layers E.M. Uram and H.E. Weber [Eds.], ASME, 53–59, 1984.
  • 4. P. W. Carpenter and J.S.B. Gajjar, A general theory for two- and three-dimensional wall mode instabilities in boundary layers over isotropic and anisotropic compliant walls, Theoret. Compt. Fluid Dyn., 1, 349–378, 1990.
  • 5. P.W. Carpenter and P. J. Morris, The effect of anisotropic wall compliance on boundary layer stability and transition, J. Fluid Mech., 218, 171–223, 1989.
  • 6. J.S.B. Gajjar and P. Sibanda, The hydrodynamic stability of channel flow compliant boundary layers, Theoret. Compt. Fluid Dyn., 8, 105–129, 1996.
  • 7. J.S.B. Gajjar and F. T. Smith, On the global instability of free disturbances with a time-dependent nonlinear viscous critical layer, J. Fluid Mech., 157, 53–77, 1985.
  • 8. R.D. Joslin, P.J. Morris and P.W. Carpenter, The role of three-dimensional instabilities in compliant wall boundary layer transition, AIAA Jour., 29, 10, 1603–1610, 1991.
  • 9. R.E. Kaplan, The stability of laminar incompressible boundary layers in the presence of compliant boundaries, Sc.D Thesis, MIT, 1965.
  • 10. S.S. Motsa, J.S.B. Gajjar and P. Sibanda, The effect of heating/cooling on the upper-branch stability of boundary layer flows over a compliant boundary, CAMES, 9, 163–181, 2002.
  • 11. J.M. Rotenberry and P.G. Saffman, Effect of compliant boundaries on weakly nonlinear shear waves in channel flows, SIAM J. Appl. Math., 50, 20, 361–394, 1990.
  • 12. S. Shateyi, P. Sibanda and S.S. Motsa, Three-dimensional stability of heated or cooled accelerating boundary layer flows over a compliant surface, ANZIAM J., 44(E), E55–E81, 2002.
  • 13. F.T. Smith, Nonlinear stability of boundary layers for disturbances of various sizes, Proc. Roy. Soc. A368, 573–589, London 1979.
  • 14. K. S. Yeo, The stability of flow over flexible surfaces, Ph.D. Thesis, University of Cambridge, 1986.
  • 15. K.S. Yeo, The stability of boundary layer flow over a single and multi-layer viscoelastic walls, J. Fluid Mech., 196, 369–408, 1989.
  • 16. K.S. Yeo, The three-dimensional stability of boundary-layer flow over compliant walls, J. Fluid Mech., 238, 537–577, 1992.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0004-0014
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