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Nonlinear evolution and breakdown in unstable boundary layers

Published online by Cambridge University Press:  19 April 2006

A. D. D. Craik
Affiliation:
Department of Applied Mathematics, University of St Andrews, Fife KY16 9SS

Abstract

The nonlinear evolution and breakdown of laminar flow in the boundary layer on a flat plate is examined with the aim of making a closer comparison of theory and experiment than has been attempted previously. The importance of three-dimensionality is emphasized. It is concluded that many features of the nonlinear instability are consistent with existing linear and weakly nonlinear theories even as breakdown is approached. The development of the secondary instability, or ‘spike’, is also considered and suggestions for an improved theory of its growth are made.

Type
Research Article
Copyright
© 1980 Cambridge University Press

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References

Antar, B. N. & Collins, F. G. 1975 Phys. Fluids 18, 289297.
Benney, D. J. 1961 J. Fluid Mech. 10, 209236.
Benney, D. J. 1964 Phys. Fluids 7, 319326.
Benney, D. J. & Lin, C. C. 1960 Phys. Fluids 3, 656657.
Bouthier, M. 1972 J. Méc. 11, 599621.
Bouthier, M. 1973 J. Méc. 12, 7695.
Corner, D., Houston, D. J. R. & Ross, M. A. S. 1976 J. Fluid Mech. 77, 81103.
Craik, A. D. D. 1971 J. Fluid Mech. 50, 393413.
Craik, A. D. D. 1979 Proc. IUTAM Symp. on Laminar-Turbulent Transition, Stuttgart. Springer.
Crow, S. C. 1966 J. Fluid Mech. 24, 153164.
Fasel, H. 1976 J. Fluid Mech. 78, 355383.
Gaster, M. 1974 J. Fluid Mech. 66, 465480.
Gaster, M. 1975 Proc. Roy. Soc. A 347, 271289.
Gaster, M. 1978 Paper presented at 12th Symp. Naval Hydrodyn. Washington D.C.
Gaster, M. & Grant, I. 1975 Proc. Roy. Soc. A 347, 253269.
Greenspan, H. P. & Benney, D. J. 1963 J. Fluid Mech. 15, 133153.
Hama, F. & Nutant, J. 1963 Proc. 1963 Heat Transfer and Fluid Mech. Inst. pp. 7793. Stanford University Press.
Herbert, T. 1975 Proc. 4th Int. Conf. on Numerical Methods in Fluid Dynamics, Lecture notes in Physics, vol. 35, pp. 212217. Springer.
Herbert, T. 1977 Proc. AGARD Conf. No. 224, Copenhagen, paper no. 3.
Holstein, H. 1950 Z. angew. Math. Mech. 30, 2549.
Itoh, N. 1974 Trans. Japan Soc. Aero. Space Sci. 17, 175186.
Itoh, N. 1977 J. Fluid Mech. 82, 455468.
Jimenez, J. & Whitham, G. B. 1976 Proc. Roy. Soc. A 439, 277287.
Jordinson, R. 1971 Phys. Fluids 14, 25352537.
Joseph, D. D. & Hung, W. 1971 Arch. Rat. Mech. Anal. 44, 122.
Kachanov, Y. S., Kozlov, V. V. & Levchenko, V. Y. 1977 Fluid Dynamics 3–4, 383390. (translation of Izv. Akad. Nauk S.S.S.R., Mekh. Zhid. i Gaza. 3, 49–58.
Kachanov, Y. S., Kozlov, V. V. & Levchenko, V. Y. 1978 A.I.A.A. Paper no. 78-1131; 11th Fluid and Plasma Dynamics Conf. Seattle, Washington.
Klebanoff, P. S. & Tidstrom, K. D. 1959 N.A.S.A. Tech. Note D-195.
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 J. Fluid Mech. 12, 134.
Komoda, H. 1967 Phys. Fluids Suppl. 10, S8794.
Kovasznay, L. S. G., Komoda, N. & Vasudeva, B. R. 1962 Proc. 1962 Heat Transfer and Fluid Mech. Inst., pp. 126. Stanford University Press.
Landahl, M. T. 1972 J. Fluid Mech. 56, 775802.
Landau, L. 1944 C. R. Acad. Sci. U.R.S.S. 44, 311314.
Mack, L. M. 1976 J. Fluid Mech. 73, 497520.
Mack, L. M. 1977 Proc. AGARD Conf. No. 224, Copenhagen, paper no. 1.
Mack, L. M. 1978 Paper presented at 12th Symp. Naval Hydrodyn., Washington, D.C.
Morkovin, M. V. 1978 AGARDograph AG-236.
Murdock, J. W. 1977 A.I.A.A. J. 15, 11671173.
Nayfeh, A. H. 1979 Effect of streamwise vortices on Tollmien-Schlichting waves. Preprint.
Nayfeh, A. H. & Bozatli, A. N. 1979 A.I.A.A. 12th Fluid and Plasma Dyn. Conf. Williamsburg, Virginia, paper 79-1496.
Nelson, G. & Craik, A. D. D. 1977 Phys. Fluids 20, 698700.
Orszag, S. A. 1976 Proc. 5th Int. Conf. on Numerical Methods in Fluid Dynamics, Lecture notes in Physics, vol. 59, pp. 3251. Springer.
Raetz, G. S. 1959 Norair Rep. NOR-59-383. Hawthorne, Calif.
Reshotko, E. 1976 Ann. Rev. Fluid Mech. 8, 311349.
Ross, J. A., Barnes, F. H., Burns, J. G. & Ross, M. A. S. 1970 J. Fluid Mech. 43, 819832.
Saric, W. S. & Nayfeh, A. H. 1975 Phys. Fluids 18, 945950.
Saric, W. S. & Reynolds, G. A. 1979 Proc. IUTAM Symp. on Laminar-Turbulent Transition, Stuttgart. Springer.
Schubauer, G. B. & Skramstad, H. K. 1948 N.A.C.A. Rep. no. 909.
Stewartson, K. 1974 Polish Acad. Sci. Fluid Dyn. Trans. 7, 101128.
Stewartson, K. & Stuart, J. T. 1971 J. Fluid Mech. 48, 529545.
Stuart, J. T. 1960 J. Fluid Mech. 9, 353370.
Stuart, J. T. 1962 Adv. Aero. Sci. 3, 121142.
Tani, I. 1969 Ann. Rev. Fluid Mech. 1, 169196.
Usher, J. R. & Craik, A. D. D. 1975 J. Fluid Mech. 70, 437461. (Appendix by F. Hendriks.)
Watson, J. 1960 J. Fluid Mech. 9, 371389.
Wortmann, F. X. 1977 Proc. AGARD Conf. No. 224, Copenhagen, paper no. 12.
Wygnanski, I., Haritonidis, J. H. & Kaplan, R. E. 1979 J. Fluid Mech. 92, 505528.