Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-14T22:33:47.910Z Has data issue: false hasContentIssue false
  • English
  • Français

On strongly nonlinear vortex/wave interactions in boundary-layer transition

Published online by Cambridge University Press:  26 April 2006

P. Hall and
F. T. Smith
P. Hall
Affiliation:
Mathematics Department, The University, Exeter EX4 4QE, UKCurrent address: Mathematics Department, The University, Manchester, M13 9PL, UK.
F. T. Smith
Affiliation:
Mathematics Department, University College, Gower Street, London WC1E 6BT, UK
Get accessRights & Permissions [Opens in a new window]

Abstract

The interactions between longitudinal vortices and accompanying waves considered here are strongly nonlinear, in the sense that the mean-flow profile throughout the boundary layer is completely altered from its original undisturbed state. Nonlinear interactions between vortex flow and Tollmien-Schlichting waves are addressed first, and some analytical and computational properties are described. These include the possibility in the spatial-development case of a finite-distance break-up, inducing a singularity in the displacement thickness. Second, vortex/Rayleigh-wave nonlinear interactions are considered for the compressible boundary layer, along with certain special cases of interest and some possible solution properties. Both types, vortex/Tollmien-Schlichting and vortex/Rayleigh, are short-scale/long-scale interactions and they have potential applications to many flows at high Reynolds numbers. Their strongly nonlinear nature is believed to make them very relevant to fully fledged transition to turbulence.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 227 , June 1991, pp. 641 - 666
Copyright
© 1991 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Bassom, A. P. & Hall, P. 1990 Stud. Appl. Maths (in press).
Bennett, J. & Hall, P. 1987 J. Fluid Mech. 188, 445.
Bennett, J., Hall, P. & Smith, F. T. 1991 J. Fluid Mech. 223, 475.
Benney, D. & Chow, C. 1989 Stud. Appl. Maths 80, 37.
Benney, D. & Lin, C. C. 1960 Phys. Fluids 3, 657.
Blackaby, N. D. 1991 On viscous, inviscid and centrifugal instability mechanisms in compressible boundary layers, including non-linear vortex/wave interactions and the effects of large Mach number on transition. Ph.D. thesis, University of London.
Blennerhassett, P. J. & Smith, F. T. 1991 To be submitted for publication.
Bowles, R. I. 1989 Ph.D. Thesis, University of London.
Brown, S. N. & Smith, F. T. 1990 J. Fluid Mech. 219, 499.
Bush, W. B. 1966 J. Fluid Mech. 25, 51.
Cowley, S. J. & Hall, P. 1990 J. Fluid Mech. 214, 17.
Craik, A. D. D. 1971 J. Fluid Mech. 50, 393.
Davey, A. 1962 J. Fluid Mech. 14, 336.
Duck, P. W. 1985 J. Fluid Mech. 160, 465.
Fasel, H., Rist, U. & Konzelmann, U. 1987 AIAA Paper 87–1203.
Gajjar, J. S. B. 1989 Submitted for publication.
Gilbert, N. & Kleiser, L. 1986 In Direct and Large Eddy Simulation of Turbulence (ed. U. Schumann & R. Friedrich), pp. 1–18. Vieweg.
Gilbert, N. & Kleiser, L. 1988 In Proc. Intl Seminar on Near-Wall Turbulence. Hemisphere.
Hall, P. 1982 J. Inst. Maths Applics. 29, 173–196.
Hall, P. 1983 J. Fluid Mech. 130, 41–68.
Hall, P. 1988 J. Fluid Mech. 193, 243.
Hall, P. & Lakin, W. D. 1988 Proc. R. Soc. Lond. A 415, 421
Hall, P. & Seddougui, S. 1989 J. Fluid Mech. 204, 405.
Hall, P. & Smith, F. T. 1984 Stud. Appl. Maths 70, 91.
Hall, P. & Smith, F. T. 1988 Proc. R. Soc. Lond. A 417, 255
Hall, P. & Smith, F. T. 1989 Eur. J. Mech. B 8, 179
Hall, P. & Smith, F. T. 1990 Proc. ICASE Workshop on Instability and Transition, Vol. II (ed. M. Y. Hussaini & R. G. Voigt), pp. 5–39. Springer.
Hama, F. R. & Nutant, J. 1963 In Proc. Heat Transfer and Fluid Mech. Inst. pp. 77–93. Stanford University Press.
Holden, M. S. 1985 AIAA Paper 85–0325.
Hoyle, J. M., Smith, F. T. & Walker, J. D. A. 1991 Comput. Phys. Commun. (in press).
Kachanov, Yu. S. & Levchenko, V. Yu 1984 J. Fluid Mech. 138, 209.
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 J. Fluid Mech. 12, 1.
Kleiser, L. & Schumann, U. 1984 Proc. ICASE Symp. on Spectral Methods (ed. R. G. Voigt, D. Gottlieb, & M. Y. Hussaini), pp. 141–163. SIAM-CBMS.
Laurien, E. & Kleiser, L. 1989 J. Fluid Mech. 199, 403.
Lee, R. S. & Cheng, H. K. 1969 J. Fluid Mech. 38, 161–179.
Mack, L. M. 1975 AIAA J. 13, 278–289.
Mack, L. M. 1984 AGARD Rep. 709.
Malik, M. R. 1982 NASA CR-165925.
Malik, M. R. 1987 AIAA Paper 87–1414.
Malkus, W. 1956 J. Fluid Mech. 1, 521.
Nishioka, M. & Asai, M. 1984 In Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi), pp. 87–92. North-Holland.
Nishika, M. & Asai, M. 1985 J. Fluid Mech. 150, 441.
Nishioka, M., Asai, M. & Iida, S. 1981 In Transition and Turbulence (ed. R. E. Meyer), pp. 113–126. Academic.
Peridier, V. J., Smith, F. T. & Walker, J. D. A. 1991a Vortex-induced boundary-layer separation. Part 1. The limit problem Rep. J. Fluid Mech. (in press).Google Scholar
Peridier, V. J., Smith, F. T. & Walker, J. D. A. 1991b Vortex-induced boundary-layer separation. Part 2. Unsteady interacting boundary-layer theory. J. Fluid Mech. (in press).Google Scholar
Seddougui, S., Smith, F. T. & Bowles, R. I. 1991 Eur. J. Mech. (in press).
Smith, F. T. 1979a Proc. R. Soc. Lond. A 368, 573
Smith, F. T. 1979b Mathematika 26, 187.
Smith, F. T. 1986 J. Fluid Mech. 169, 353.
Smith, F. T. 1988 Mathematika 35, 256–273.
Smith, F. T. 1989 J. Fluid Mech. 198, 127.
Smith, F. T. 1991 Computers & Fluids (to appear). (Proc. R. T. Davis Memorial Symp., Cincinnati, 1987).
Smith, F. T. & Burggraf, O. R. 1985 Proc. R. Soc. Lond. A 399, 25
Smith, F. T., Doorly, D. J. & Rothmayer, A. P. 1990 Proc. R. Soc. Lond. A 428, 255
Smith, F. T. & Stewart, P. A. 1987 J. Fluid Mech. 179, 227.
Smith, F. T. & Walton, A. G. 1989 Mathematika 36, Part 2, 262.
Spalart, P. R. & Yang, K. S. 1987 J. Fluid Mech. 178, 345–365.
Stewartson, K. 1964 The Theory of Laminar Boundary Layers in Compressible Fluids. Oxford University Press.
Stuart, J. T. 1960 J. Fluid Mech. 9, 383.
Thomas, A. S. W. 1987 In Proc. 10th US Natl. Congress on Applied Maths, pp. 436–444. ASME.
Walton, A. G. 1991 Theory and computation of three-dimensional nonlinear effects in pipe flow transition. Ph.D. thesis, University of London.
Watson, J. 1960 J. Fluid Mech. 9, 371.
Williams, D. R. 1987 In Stability of Time Dependent and Spatially Varying Flows (ed. D. L. Dwoyer & M. Y. Hussaini), pp. 335–350. Springer.
Williams, D. R., Fasel, H. & Hama, F. R. 1984 J. Fluid Mech. 149, 179.
Wray, A. A. & Hussaini, M. Y. 1984 Proc. R. Soc. Lond. A 392, 393
Zang, T. A. & Hussaini, M. Y. 1986 Appl. Math. Comput. 19, 359.
Zang, T. A. & Hussaini, M. Y. 1987 In Nonlinear Wave Interactions in Fluids (ed. R. W. Miksad, T. R. Akylas, T. Herbert), pp. 131–145. ASME.
Zang, T. A. & Krist, S. E. 1989 Theor. Comput. Fluid Dyn. 1, 41.