Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T04:33:30.748Z Has data issue: false hasContentIssue false
  • English
  • Français

Properties of strongly nonlinear vortex/Tollmien–Schlichting-wave interactions

Published online by Cambridge University Press:  26 April 2006

A. G. Walton  and
F. T. Smith
A. G. Walton
Affiliation:
Department of Mathematics, Imperial College, London SW7 2BZ, UK
F. T. Smith
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

An analytical and computational study is presented on solution properties of strongly nonlinear vortex/wave interactions involving Tollmien–Schlichting waves, in boundary-layer transition. The longitudinal vortex part, i.e. the total mean flow, is governed by a three-dimensional vortex system but coupled, through an effective spanwise slip condition at the surface, with the accompanying wave part, so that both the vortex and the wave parts are unknowns. Terminal forms of the space-marching or time-marching problem are proposed first, yielding either a lift-off separation singularity or a strong-attachment singularity. Second, a similarity version of the complete system is addressed numerically and analytically. This leads to a number of interesting solution features as the typical wave pressure is increased into the strongly nonlinear regime. In particular, lift-off separation and attachment forms seem to emerge which are analogous with those proposed above. The flow developments beyond the terminal forms are discussed, together with the links of the work with recent computational results and, tentatively, with experimental observations including the creation of lambda vortices (as a form of lift-off separation).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 244 , November 1992 , pp. 649 - 676
Copyright
© 1992 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.)

References

Aihara Y., Tomita, Y. & Ito A. 1985 In Laminar–Turbulent Transition (ed. V. V. Kozlov), p. 477. Springer.
Bennett J., Hall, P. & Smith F. T. 1991 J. Fluid Mech. 223, 475.
Brown P. G., Brown, S. N. & Smith F. T. 1992 On the starting process of strongly nonlinear vortex/Rayleigh-wave interactions. Mathematika (submitted).Google Scholar
Cebeci T., Stewartson, K. & Schimke, S. M. 1984 J. Fluid Mech. 147, 315.
Elliott J. W., Cowley, S. J. & Smith F. T. 1983 Geophys. Astrophys. Fluid Dyn. 25, 77.
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 In Instability and Transition (ed. M. Y. Hussaini & R. G. Voigt). Springer.
Hall, P. & Smith F. T. 1991 J. Fluid Mech. 227, 641.
Holden M. S. 1985 AIAA Paper 85–0325.
Hoyle J. M. 1991 Extensions to the theory of finite-time breakdown of unsteady interactive boundary layers. Ph.D. thesis, University of London.
Hoyle J. M., Smith, F. T. & Walker J. D. A. 1991 Comput. Phys. Commun. 65, 151.
Hoyle J. M., Smith, F. T. & Walker J. D. A. 1992 On sublayer eruption and vortex formation; part 2 (in preparation).
Kachanov Y. S., Ryzhov, O. S. & Smith F. T. 1992 Formation of solitons in transitional boundary layers: theory and experiments J. Fluid Mech. (submitted).
Nishioka M., Asai, N. & Iida S. 1979 In Laminar–Turbulent Transition (ed. R. Eppler & H. Fasel). Springer.
Peridier V. J., Smith, F. T. & Walker J. D. A. 1991a J. Fluid Mech. 232, 99.
Peridier V. J., Smith, F. T. & Walker J. D. A. 1991b J. Fluid Mech. 232, 133.
Reid W. H. 1965 In Basic Developments in Fluid Dynamics, vol. 1 (ed. M. Holt), p. 249. Academic.
Simpson, C. J. & Stewartson K. 1982a Z. Angew. Math. Phys. 33, 370.
Simpson, C. J. & Stewartson K. 1982b Q. J. Mech. Appl. Maths 35, 291.
Smith F. T. 1979a Proc. R. Soc. Lond. A 366, 91.
Smith F. T. 1979b Proc. R. Soc. Lond. A 368, 573.
Smith F. T. 1988 Mathematika 35, 256.
Smith F. T. 1989 J. Fluid Mech. 198, 127.
Smith F. T. 1991 AIAA Paper 91–0331 (and AIAA J. to appear).
Smith, F. T. & Blennerhassett P. 1992 Proc. R. Soc. Lond. A 436, 585.
Smith, F. T. & Bowles R. I. 1992 Transition theory and experimental comparisons on (a) amplification into streets and (b) a strongly nonlinear break-up criterion Proc. Roy. Soc. A (submitted).
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 425, 255.
Smith, F. T. & Stewart P. A. 1987 J. Fluid Mech. 179, 227.
Smith, F. T. & Walton A. G. 1989 Mathematika 36, 262.
Stewart, P. A. & Smith F. T. 1992 J. Fluid Mech. 244, 79.
Swearingen, J. D. & Blackwelder R. F. 1987 J. Fluid Mech. 182, 255.
Sychev V. V. 1979 Isv. Akad. Nauk. SSSR Mech. Zhid. Gaza 6, 21.
Walton A. G. 1991 Theory and computation of three-dimensional nonlinear effects in pipe flow transition. Ph.D. thesis, University of London.