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On the nonlinear growth of single three-dimensional disturbances in boundary layers

Published online by Cambridge University Press:  26 February 2010

F. T. Smith ,
P. A. Stewart  and
R. G. A. Bowles
F. T. Smith
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT
P. A. Stewart
Affiliation:
D.A.M.T.P., Silver Street, Cambridge, CB3 9EW
R. G. A. Bowles
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT
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Summary

Experiments indicate the importance of three-dimensional action during transition, while high-Reynolds-number-flow theory indicates a multi-structured type of analysis. In line with this, the three-dimensional nonlinear unsteady triple-deck problem is addressed here, for slower transition. High-amplitude/high-frequency properties show enhanced disturbance growth occurring downstream for single nonlinear oblique waves inclined at angles greater than tan−1 √2 (≈54.7°) to the free stream, in certain interesting special cases. The three-dimensional response there is very ‘spiky’ and possibly random, with sideband instabilities present. A second nonlinear stage, and then an Euler stage, are entered further downstream, although faster transition can go straight into these more nonlinear stages. More general cases are also considered. Sideband effects, sublayer bursting and secondary instabilities are discussed, along with the relation to experimental observations.

Type
Research Article
Information
Mathematika , Volume 41 , Issue 1 , June 1994 , pp. 1 - 39
Copyright
Copyright © University College London 1994

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References

1.Klebanoff, P. S., Tidstrom, K. D. and Sargent, L. M.. J. Fluid Mech., 12 (1962), 1.Google Scholar
2.Wygnanski, I., Sokolov, M. and Friedman, D.. J. Fluid Mech., 78 (1976), 785.Google Scholar
3.Kachanov, Yu. S. and Levchenko, V. Ya.. J. Fluid Mech., 138 (1984), 209.Google Scholar
4.Gaster, M.. Proc. Symp. on Turb. and Chaotic Phen. in Fluids, Kyoto, Japan (ed. Tatsumi, T.) (Elsevier, 1984); see also Transition and Turbulence, 95, ed. S. E. Meyer (Academic Press, 1981).Google Scholar
5.Saric, W. S., Kozlov, V. V. and Levchenko, V. Ya.. A1AA Paper No. 84-0007 (presented January 1984, Reno, Nevada).Google Scholar
6.Herbert, T.. AIAA Paper No. 84-0009 (presented January 1984, Reno, Nevada).Google Scholar
7.Craik, A. D. D.. J. Fluid Mech., 50 (1971), 393; see also Craik, 1984, Proc. IUTAM Symp. on Lam.-Turb. Transition, Novosibirsk, USSR, (ed. V. V. Kozlov) (Springer-Verlag, 1985).Google Scholar
8.Smith, F. T. and Burggraf, O. S.. Proc. Roy. Soc. A, 399 (1985), 25.Google Scholar
9.Smith, F. T.. Utd. Tech. Res. Center, E. Hartford, Conn., Rept. UTRC85-36, 1985, and J. Flui Mech., 1986.Google Scholar
10.Duck, P. W.. J. Fluid Mech., 160 (1985), 465.CrossRefGoogle Scholar
11.Smith, F. T.. Proc. Roy. Soc. A, 366 (1979), 91 and A, 368 (1979), 573.Google Scholar
12.Goldstein, M. E.. J. Fluid Mech., 154 (1985), 509–530.CrossRefGoogle Scholar
13.Hall, P. and Smith, F. T.. Stud, in Appl. Math., 70 (1984), 91.CrossRefGoogle Scholar
14.Criminale, W. O. and Kovasnay, L. S. G.. J. Fluid Mech., 14 (1962), 59.Google Scholar
15.Hall, P.. Proc. Roy. Soc. A, 406 (1986), 93–106.Google Scholar
16.Stewart, P. A. and Smith, F. T.. Proc. Roy. Soc. A, 409 (1987), 229–248.Google Scholar
17.Smith, F. T., Papageorgiou, D. and Elliott, J. W.. J. Fluid Mech., 146 (1984).Google Scholar
18.Itoh, N.. Trans. Jap. Soc. Aerosp. Sc, 17 (1974), 175.Google Scholar
19.Bretherton, C. S. and Spiegel, E. A.. Phys. Letters, 96A (1983), 152.CrossRefGoogle Scholar
20.Moon, H. T., Huerre, P. and Redekopp, L. G.. Phys. Rev. Letter, 49 (1982), 48.Google Scholar
21.Kuramoto, Y.. Suppl. of Progress of Theor. Phys., No. 64 (1978), 346.CrossRefGoogle Scholar
22.Doorly, D. J.. D. Phil. Thesis, Univ. of Oxford, 1983; see also: D. J. Doorly and M. L. C. Oldfield, ASME paper 85-GT-112, (1985), presented at ASME Gas Turbine Conf., Houston, Texas, March 1985 (and Trans. ASME Eng. for Power (1986)); and D. J. Doorly, M. L. G. Oldfield and C. T. J. Scrivener, AGARD C.P.P. 390 (1985), presented at AGARD Mtg., Bergen, Norway, May 1985.Google Scholar
23.Smith, F. T. and Stewart, P. A.. J. Fluid Mech., 179 (1987), 227–252.Google Scholar
24.Bodonyi, R. J. and Smith, F. T.. Proc. Roy. Soc. A, 375 (1981), 65.Google Scholar
25.Walker, J. D. A. and Scharnhorst, R. K.. In Recent Adas, in Eng. Sci., ed. Sih, G. C., 541, (Univ. Press, Bethlehem, Penn., 1977); see also Walker & Abbott, in Turb. in Int. Flows, ed. S. N. B. Murthy, 131 (1977), (Hemisph. Pub. Corp., Wash., 1977).Google Scholar
26.Fasel, H.. Proc. Symp. on Turb. & Chaotic Phen. in Fluids, Kyoto, Japan, ed. Tatsumi, T. (Elsevier, 1984).Google Scholar
27.Smith, F. T. and Bodonyi, R. J.. Aeron. Ml. of Roy Aeron. Soc, June/July (1985), 205–212.Google Scholar
28.Davey, A., Hocking, L. M. and Stewartson, K.. J. Fluid Mech., 63 (1974), 529.CrossRefGoogle Scholar
29.Stewart, P. A.. Ph.D. Thesis, Univ. of London, in preparation.Google Scholar
30.Smith, F. T.. Proc. Symp. on Stability of Time-Dependent and Spatially Varying Flows, NASA Langley Res. Cent., Hampton, VA., Aug. 1985, (Springer-Verlag, 1986) see also United. Tech. Res. Cent., East Hartford, Rept. UTRC85-55.Google Scholar
31.Stern, M. E. and Paldor, N.. Phys. Fluids, 26 (1983), 906.CrossRefGoogle Scholar
32.Kovasznay, L. S. G., Komoda, H. and Vasudiva, R. B.. Heat Transfer & Fluid Mech. Inst., ed. Elles, F. E., Kauzlarich, J., Sleicher, C. A. and Street, S. (Stanford Univ. Press, CA, 1962).Google Scholar
33.Benney, D. J.. Proc. Symp. on time-dependent and spatially varying flows, NASA Langley Res. Cent., Hampton, VA, Aug. 1985 (Springer-Verlag, 1986).Google Scholar
34.Stewart, P. A. and Smith, F. T.. J. Fluid Mech., 244 (1992), 79–100.Google Scholar
35.Smith, F. T.. Mathematika 35 (1988), 256–273.CrossRefGoogle Scholar
36.Smith, F. T. and Bowles, R. I.. Proc. Roy Soc. A, 439 (1992), 163.Google Scholar
37.Kachanov, Y. S., Ryzhov, O. S. and Smith, F. T.. J. Fluid Mech., 251 (1993), 273.CrossRefGoogle Scholar
38.Davis, D. A. R.. On linear and nonlinear instability in boundary layers with crossflow. Ph.D. Thesis, Univ. of London (1992).Google Scholar
39.Hoyle, J. M.. Extensions to the theory of finite-time breakdown of unsteady interactive boundary layers. Ph.D. Thesis, Univ. of London (1992).Google Scholar
40.Peridier, V. J., Smith, F. T. and Walker, J. D. A.. J. Fluid Mech., 232 (1992), 99–131 & 133-165.CrossRefGoogle Scholar
41.Hoyle, J. M., Smith, F. T. and Walker, J. D. A.. Comput. Phys. Commns., 65 (1991), 151–157.CrossRefGoogle Scholar
42.Goldstein, M. E. & Hultgren, L. S.. Ann. Rev. Fluid Mech. 21 (1989), 137–166.Google Scholar
43.Smith, F. T. and Blennerhassett, P.. Proc. Roy. Soc. A, 436 (1992), 585–602.Google Scholar
44.Rothmayer, A. P. and Smith, F. T.. Trans. A.S.M.E. Conf, Cincinnati, Ohio, June, 1987 (1987).Google Scholar
45.Smith, F. T., Doorly, D. J. and Rothmayer, A. P.. Proc. Roy. Soc. A, 428 (1990), 255–281.Google Scholar
46.Smith, C. S., Walker, J. D. A., Haidari, A. H. and Sobrun, U.. Trans. Roy. Soc. A, 336 (1991), 131–175.Google Scholar
47.Smith, F. T.. Utd. Techn. Res. Center Rept. 86–10 (1986).CrossRefGoogle Scholar
48.Klebanoff, P. S. and Tidstrom, K. D.. Tech. Notes, Nat. Aero. Space Admin. Wash. D-195, (1959).Google Scholar