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Nonlinear Breakdowns in Boundary Layer Transition

  • Frank T. Smith
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

Theoretical studies of boundary-layer transition are described, based on high Reynolds numbers and with attention drawn to nonlinear interactions, breakdowns and scales. The article notes in particular truly nonlinear theories for which the mean-flow profile is completely altered from its original state. Two- and three-dimensional flow theory and conjectures on turbulent boundary-layer structures are included. Specific recent findings noted, and in qualitative agreement with experiments, are: nonlinear finite-time break-ups in unsteady interactive boundary layers; strong vortex/wave interactions; and prediction of turbulent boundary-layer displacement-and stress sublayer-thicknesses.

Keywords

Turbulent Boundary Layer Nonlinear Interaction Interactive Boundary Layer Nonlinear Disturbance Spanwise Wavenumbers 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Smith, F.T. and Burggraf, O.R., Proc. Roy. Soc. A399 (1985) 25–55.ADSMATHCrossRefGoogle Scholar
  2. [2]
    Brotherton-Ratcliffe, R.V. and Smith, F.T., Mathematika 34 (1987) 86–100.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Smith, F.T., Mathematika 35 (1988), 256–273.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Hall, P. and Smith, F.T., Proc. Roy. Soc. A417 (1988) 255–282. Also, ICASE Rept. (1987).Google Scholar
  5. [5]
    Hall, P. and Smith, F.T., ICASE Rept. (1988) 88–46 and European J. Mechs. B 8 (1989) 179–205.Google Scholar
  6. [6]
    Smith, F.T. Doorly, D.J. and Rothmayer, A.P., Proc. Roy. Soc. A (1989), submitted. Also, Rept. (1987) UTRC 87–43.Google Scholar
  7. [7]
    Smith, F.T., Papageorgiou, D.T. and Elliott, J.W., J. Fluid Mech. 146 (1984) 313–330.ADSMATHCrossRefGoogle Scholar
  8. [8]
    Conlisk, A.T., Burggraf, O.R. and Smith, F.T., Trans. A.S.M.E. (1987), Forum on Unsteady Separation, Cincinnati, Ohio, U.S.A., June 1987.Google Scholar
  9. [9]
    Duck, P.W., J. Fluid Mech. 160 (1985) 465.MathSciNetADSMATHCrossRefGoogle Scholar
  10. [10]
    Smith, F.T., United Tech. Res. Cent., E. Hartford, Ct., U.S.A., Rept. UTRC85–36 (1985)Google Scholar
  11. Smith, F.T., A.I.A.A. paper no. 84–1582 (1984)Google Scholar
  12. Smith, F.T., J. Fluid Mech. 169 (1986) 353–377 ).ADSMATHCrossRefGoogle Scholar
  13. [11]
    Smith, F.T., Proc. Roy. Soc. A 420 (1988), 21–52. Also, Rept. (1988) UTRC 88–12.Google Scholar
  14. [12]
    Walker, J.D.A. and Abbott, D.E., in Turb. in Internal Flows (ed. S.N.B. Murthy ), Hemisph. Pub. Corp., Wash. (1977).Google Scholar
  15. [13]
    Fasel, H., Proc. Symp. on Turb. & Chaotic Phen. in Fluids (ed. T. Tatsumi ), Elsevier (1984).Google Scholar
  16. [14]
    Orszag, S.A. and Patera, A.T., J. Fluid Mech. 128 (1983) 347.ADSMATHCrossRefGoogle Scholar
  17. [15]
    Craik, A.D.D., Proc. IUTAM Symp. on Lam.-Turb. transition (ed. V.V. Kozlov ), Springer-Verlag (1985).Google Scholar
  18. [16]
    Smith, F.T. and Stewart, P.A., United Tech. Res. Cent. E. Hartford, Ct., U.S.A., Rept. UTRC 86–26 (1986) (also J. Fluid Mech. 179 (1987) 227–252 ).Google Scholar
  19. [17]
    Stewart, P.A., Ph.D. thesis, Univ. of London (1989), in preparation.Google Scholar
  20. [18]
    Kachanov, Y.S. and Levchenko, V.Y., J. Fluid Mech. 138 (1984) 209.ADSCrossRefGoogle Scholar
  21. [19]
    Smith, F.T., On Transition to Turbulence in Boundary Layers, in: European Conference on Turbulence (Springer-Verlag 1987 ). Also, Utd. Tech. Cent., E. Hartford, Ct., U.S.A., Rept. (1986) UTRC 86–10.Google Scholar
  22. [20]
    Smith, F.T., Computers & Fluids, Volume dedicated to R.T. Davis (1989), to appear; and presentation, R.T. Davis Memorial Symposium, Cincinnati (1987).Google Scholar
  23. [21]
    Smith, F.T., J. Fluid Mech. 198 (1989), 127–153. Also, Rept. UTRC (1987) 87–52.Google Scholar
  24. [22]
    Klebanoff, P.S., Tidstrom, K.D. and Sargent, L.M., J. Fluid Mech. 12 (1962)Google Scholar
  25. [23]
    Gad-el-Hak, M., Blackwelder, R.E. and Riley, J.J., J. Fluid Mech. 110 (1981) 73.ADSCrossRefGoogle Scholar
  26. [24]
    Riley, J.J. and Gad-el-Hak, M., in Frontiers in Fluid Mechanics (eds. S.H. Davis and J.L. Lumley, 1985 ).Google Scholar
  27. [25]
    Cebeci, T. and Smith, A.M.O., Turbulent Shear Flows ( Academic Press, New York, 1974 ).Google Scholar
  28. [26]
    Wygnanski, I.J. and Champagne, F.H., J. Fluid Mech. 59 (1973) 281.ADSCrossRefGoogle Scholar
  29. [27]
    Wygnanski, I.J., Sokolov, M. and Friedman, D., J. Fluid Mech. 69 (1975) 283.ADSCrossRefGoogle Scholar
  30. [28]
    Smith, F.T. and Walton, A.G., Mathematika 36 (1989), part 2, and ICASE Rept. (1988) 88–66Google Scholar
  31. Hall, P. and Smith, F.T., ICASE Rept. (1989), in preparationGoogle Scholar
  32. Smith, F.T., Theor. & Comp. Fluid Dyn. (1990), Proc. Workshop on Instability and Transition, May 1989, to appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Frank T. Smith
    • 1
  1. 1.Department of MathematicsUniversity College LondonLondonUK

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