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On effects of increasing amplitude in a boundary-layer spot

Published online by Cambridge University Press:  26 February 2010

B. T. Dodia ,
R. G. A. Bowles  and
F. T. Smith
B. T. Dodia
Affiliation:
Department of Aeronautics, Imperial College, London SW7 2AZ.
R. G. A. Bowles
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT.
F. T. Smith
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT.
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Abstract

The boundary-layer spots involved here come from large-time theory and related computations on the Euler equations to cover the majority of the global properties of the spot disturbances, which are nonlinear, three-dimensional, and transitional rather than turbulent. The amplitude levels investigated are higher than those examined in detail previously and produce a new near-wall momentum contribution in the mean flow, initially close to the wingtips of the spot. This enables the amplitude levels in the analysis to be raised successively, a process which gradually causes the wing-tip region to spread inwards. The process is accompanied by subtle increases in the induced phase variations. Among other things the work finds the details of how nonlinear effects grow from the wing-tips to eventually alter the entire trailing edge, and then the centre of the spot, in a strongly nonlinear fashion. Comparisons with earlier suggestions and with experiments are described at the end.

Type
Research Article
Information
Mathematika , Volume 45 , Issue 1 , June 1998 , pp. 1 - 24
Copyright
Copyright © University College London 1998

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References

1.Clark, J. P., Jones, T. V. and LaGraff, J. E.. J. Eng. Maths., 28 (1994), 1–19.CrossRefGoogle Scholar
2.Henningson, D. S., Johansson, A. V. and Alfredsson, P. H., J. Eng. Maths., 28 (1994), 21–42.CrossRefGoogle Scholar
3.Seifert, A., Zilberman, M. and Wygnanski, I.. J. Eng. Maths., 28 (1994), 43–54.CrossRefGoogle Scholar
4.Shaikh, F. N. and Gaster, M.. J. Eng. Maths., 28 (1994), 55–71.CrossRefGoogle Scholar
5.Smith, F. T., Dodia, B. T. and Bowles, R. G. A.. J. Eng. Maths., 28 (1994), 73–91.CrossRefGoogle Scholar
6.Bowles, R. G. A. and Smith, F. T., J. Fluid Mech., 295 (1995), 395–407.CrossRefGoogle Scholar
7.Emmons, H. W.. J. aeronaut. Sci., 18 (1951), 490–498; see also J. Fluid Mech., 9 (1963), 235–246.CrossRefGoogle Scholar
8.Schubauer, G. B. and Klebanoff, P. S.. NACA Rep., 1289 (1956).Google Scholar
9.Lighthill, M. J.. Introduction to boundary layer theory. Laminar boundary layers (ed. L. Rosenhead), Ch. II (Oxford University Press, 1963).Google Scholar
10.Schlichting, H.. Boundary-layer theory, 4th edn. (New York: McGraw-Hill, 1979).Google Scholar
11.Falco, R. E., Ch. 1.1-1.4 In Proc. 6th Biennial Symp. Turb. (University of Missouri-Rolla, 1979).Google Scholar
12.Head, M. R. and Bandyopadhyay, P.. J. Fluid Mech., 107 (1981), 297–338.CrossRefGoogle Scholar
13.Perry, A. E., Liu, T. T. and Teh, E. W.. J. Fluid Mech., 104 (1981), 387–405.CrossRefGoogle Scholar
14.Chambers, F. W. and Thomas, A. S. W.. Physics Fluids, 26 (1983), 1160–1162.CrossRefGoogle Scholar
15.Smith, C. R., Walker, J. D. A., Haidari, A. H. and Sobrun, U.. Phil. Trans. R. Soc. Lond. A, 336 (1991), 131–175.Google Scholar
16.Gad-el-Hak, M., Blackwelder, R. F. and Riley, J. J.. J. Fluid Mech., 110 (1981), 73–95.CrossRefGoogle Scholar
17.Katz, T., Seifert, A. and Wygnanski, I. J.. J. Fluid Mech., 221 (1990), 1–22.CrossRefGoogle Scholar
18.Johansson, A. V., Her, J. and Haritonidis, J. H.. J. Fluid Mech., 175 (1987) 119–142.CrossRefGoogle Scholar
19.Henningson, D. S. and Alfredson, P. H.. J. Fluid Mech., 178 (1987), 405–421.CrossRefGoogle Scholar
20.Robinson, S. K.. Ann. Rev. Fluid Mech., 23 (1991), 601–639.CrossRefGoogle Scholar
21.Elder, J. W.. J. Fluid Mech., 9 (1960), 235.CrossRefGoogle Scholar
22.Leonard, A.. Springer Lecture Notes in Physics, 136 (1981), 119–145.CrossRefGoogle Scholar
23.Bullister, E. T. and Orszag, S. A.. J. scient. Comput., 2 (1987), 263–281.CrossRefGoogle Scholar
24.Henningson, D. S., Spalart, P. and Kim, J.. Physics Fluids, 30 (1987), 2914–2917.CrossRefGoogle Scholar
25.Henningson, D. S. and Kim, J.. J. Fluid Mech., 228 (1991), 183–205.Google Scholar
26.Lundbladh, A. and Johansson, A. V.. J. Fluid Mech., 229 (1991), 499–516.CrossRefGoogle Scholar
27.Fasel, H.. In Laminar-turbulent transition (ed. D. Arnal and R. Michel) (Berlin: Springer, 1990).Google Scholar
28.Konzelmann, U. and Fasel, H.. Proc. R. Aero. Soc. Meeting on Transition, Cambridge, U.K (1991).Google Scholar
29.Doorly, D. J. and mith, F. T.. J. Eng. Maths., 26 (1992), 87–106.CrossRefGoogle Scholar
30.Smith, F. T., Phil. Trans. Roy. Soc, A340 (1992), 131–165.Google Scholar
31.Dodia, B. T., Ph.D. thesis (Univ. of London, 1994)Google Scholar
32.Smith, F.T.. Phil. Trans. Roy. Soc, A352 (1995), 405–424.Google Scholar
33.Hall, P. and Smith, F. T.. J. Fluid Mech., 227 (1991), 641–666.CrossRefGoogle Scholar