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Short-scale effects on model boundary-layer spots

Published online by Cambridge University Press:  26 April 2006

R. G. A. Bowles  and
F. T. Smith
R. G. A. Bowles
Affiliation:
School of Mathematics and Statistics, University of Middlesex, London N11 2NQ, UK
F. T. Smith
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
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Abstract

This theoretical work, on the spot in an otherwise laminar boundary layer, concerns the initial-value problem for three-dimensional inviscid disturbances covering a wide range of scales. The study asks whether or not comparatively short scales can have a substantial impact on the spot spreading rate, as well as on other important features including the spot structure. It is found that such scales act to reduce the spread angle to approximately 11°, close to the experimental observations for transitional/turbulent spots, as opposed to the angle of 19.47° for waves near or behind the spot trailing edge. The scales emerge from coupling uniform shear flow directly with the local uniform stream and then analysing large-time features. The leading edge and trailing edge of the spot are also examined in detail, along with other structural properties. It is concluded that nonlinearity and short-scale effects probably combine to restrict the global spread angle as above, while viscous sublayer bursting among other things completes the spot structure. Related work on nonlinear, trailing-edge and leading-edge behaviours and comparisons with experiments are also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 295 , 25 July 1995 , pp. 395 - 407
Copyright
© 1995 Cambridge University Press

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References

Cheng, H. K. & Johnson, E. R. 1982 Inertial waves above an obstacle in an unbounded rapidly rotating fluid. Proc. R. Soc. Lond. A 383, 71.Google Scholar
Craik, A. D. D. 1971 Nonlinear resonant instability in boundary layers. J. Fluid Mech. 50, 393.Google Scholar
Dodia, B. T., Bowles, R. G. A. & Smith, F. T. 1995 On effects of increasing amplitudes in a boundary-layer spot. J. Engng Maths (submitted).Google Scholar
Doorly, D. J. & Smith, F. T. 1992 Initial-value problems for spot disturbances in incompressible or compressible boundary layers. J. Engng Maths 26, 87.Google Scholar
Elder, J. W. 1960 An experimental investigation of turbulent spots and breakdown to turbulence. J. Fluid Mech. 9, 235.Google Scholar
Emmons, H. W. 1951 The laminar-turbulent transition in a boundary layer, Part 1. J. Aero. Sci. 18, 490.Google Scholar
Gad-El-Hak, M., Blackwelder, R. F. & Riley, J. J. 1981 On the growth of turbulent regions in laminar boundary layers. J. Fluid Mech. 110, 73.Google Scholar
Gaster, M. 1968 The development of three-dimensional wave-packets in a boundary layer. J. Fluid Mech. 32, 173.Google Scholar
Gaster, M. 1975 A theoretical model of a wave-packet in the boundary layer on a flat plate. Proc. R. Soc. Lond. A 347, 271.Google Scholar
Gaster, M. & Grant, I. 1975 An experimental investigation of the formation and development of a wave-packet in a laminar boundary layer. Proc. R. Soc. Lond. A 347, 253.Google Scholar
Glezer, A., Katz, Y. & Wygnanski, I. 1989 On the breakdown of the wave-packet trailing a turbulent spot in a laminar boundary layer. J. Fluid Mech. 198, 1.Google Scholar
Goldstein, M. E. & Hultgren, L. S. 1988 Nonlinear spatial evolution of an externally excited instability wave in a free shear layer. J. Fluid Mech. 197, 295.Google Scholar
Henningson, D., Lundbladh, A. & Johansson, A. V. 1993 A mechanism for by-pass transition from localized disturbances in wall-bounded shear flows. J. Fluid Mech. 250, 169.Google Scholar
Kachanov, Y. S., Ryzhov, O. S. & Smith, F. T. 1993 Formation of solitons in transitional boundary layers: theory and experiment. J. Fluid Mech. 251, 273.Google Scholar
Katz, Y., Seifert, A. & Wygnanski, I. 1990 On the evolution of the turbulent spot in a laminar boundary layer with a favourable pressure gradient. J. Fluid Mech. 221, 1.Google Scholar
Lighthill, M. J. 1978 Ship waves. In Waves In Fluids (ch. 3.10). Cambridge University Press.
Mautner, T. S. & Van Atta, C. W. 1982 An experimental study of the wall-pressure field associated with a turbulent spot in a boundary layer. J. Fluid Mech. 118, 59.Google Scholar
Ryzhov, O. S. & Savenkov, V. I. 1987 Asymptotic theory of a wave packet in a boundary layer on a plate. Prikl. Matem. Mekhan. 50, 820.Google Scholar
Smith, F. T. 1986 Steady and unsteady 3D interactive boundary layers. Computers Fluids 20, 293.Google Scholar
Smith, F. T. 1992 On nonlinear effects near the wingtips of an evolving boundary-layer spot. Phil. Trans. R. Soc. Lond. A 340, 131.Google Scholar
Smith, F. T., Brown, S. N. & Brown, P. G. 1993 Initiation of three-dimensional nonlinear transition paths from an inflectional profile. Eur. J. Mech. 12, 447.Google Scholar
Smith, F. T. & Burggraf, O. R. 1985 On the development of large-sized short-scaled disturbances in boundary layers. Proc. R. Soc. Lond. A 399, 25.Google Scholar
Smith, F. T., Dodia, B. T. & Bowles, R. G. A. 1994 On global and internal dynamics of spots: a theoretical approach. J. Engng Maths 28, 73.Google Scholar
Smith, F. T., Doorly, D. J. & Rothmayer, A. P. 1990 On displacement thickness, wall-layer and mid-flow scales in turbulent boundary layers and slugs of vorticity in pipes and channels. Proc. R. Soc. Lond. A 428, 255.Google Scholar
Widnall, S. E. 1984 Growth of turbulent spot in plane Poiseuille flow. In Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi), p. 93. Elsevier.