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On the resonant nature of the breakdown of a laminar boundary layer

Published online by Cambridge University Press:  21 April 2006

Yu. S. Kachanov
Yu. S. Kachanov
Affiliation:
Institute of Theoretical and Applied Mechanics, Siberian Branch of USSR Academy of Sciences, Novosibirsk, USSR
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Abstract

The first part of this paper (§2) briefly reviews the history of the idea of the resonant nature of laminar-boundary-layer breakdown. In the second part a new wave-resonance concept of the breakdown mechanism is proposed. The existing experimental data on the laminar boundary layer (and plane channel flow) breakdown are analysed from the viewpoint of this concept and are compared with the well-known local high-frequency secondary-instability concept. The results testify to the correctness of the proposed wave-resonant concept for the initial stages of breakdown, in particular for the K-regime of transition up to the spike formation and its doubling.

Within the framework of the wave-resonance concept, before constructing the corresponding theory, many important features of the disturbance development can be qualitatively explained and understood. Concerning the understanding of the spike appearance, the wave-resonance concept complements the local high-frequency secondary-instability one and represents by itself a new fruitful viewpoint on this phenomenon. The development of the wave-resonance concept and its application to the analysis of numerical and physical experiments, together with the construction on this basis of the corresponding theory, can give an essential impetus towards the better understanding of the breakdown nature.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 184 , November 1987 , pp. 43 - 74
Copyright
© 1987 Cambridge University Press

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References

Betchov, R. 1960 On the mechanism of turbulent transition. Phys. Fluids 3, 1026.Google Scholar
Craik, A. D. D. 1971 Nonlinear resonant instability in boundary layers. J. Fluid Mech. 50, 393.Google Scholar
Craik, A. D. D. 1978 Evolution in space and time of resonant wave triads. II. A class of exact solutions. Proc. R. Soc. Lond. A 363, 257.Google Scholar
Craik, A. D. D. 1980 Nonlinear evolution and breakdown in unstable boundary layers. J. Fluid Mech. 99, 247.Google Scholar
Eppler, R. & Fasel, H. (ed.) 1980 Laminar–Turbulent Transition. Springer.
Gertsenshtein, S. Ya. 1969 On stability of a nonstationary unidirectional parallel flow of ideal liquid. Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza 2, 5 (in Russian).Google Scholar
Gilyov, V. M., Kachanov, Yu. S. & Kozlov, V. V. 1981 A development of a spatial wave packet in a boundary layer. Preprint 34, Novosibirsk, ITPM SO AN SSSR (in Russian). (See also Kachanov, Yu. S., Development of special wave packets in boundary layers. In Kozlov, 1985, p. 115.)
Greenspan, H. P. & Benney, D. J. 1963 On shear-layer instability, breakdown and transition. J. Fluid Mech. 15, 133.Google Scholar
Herbert, T. 1983 Secondary instability of plane channel flow to subharmonic three-dimensional disturbances. Phys. Fluids 26, 4.Google Scholar
Herbert, T. 1984 Analysis of the subharmonic route to transition in a boundary layer. AIAA-84-0009.
Itoh, N. 1981 Secondary instability of laminar flows. Proc. R. Soc. Lond. A 375, 565.Google Scholar
Kachanov, Yu. S., Kozlov, V. V. & Levchenko, V. Ya. 1975 Generation and development of small amplitude disturbances in a boundary layer under acoustic excitation. Rep. Siberian Div. Acad. Sci. USSR 13, 18 (in Russian).Google Scholar
Kachanov, Yu. S., Kozlov, V. V. & Levchenko, V. Ya. 1977 Nonlinear development of a wave in a boundary layer. Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza 3, 49 (in Russian). (See also Fluid Dyn. 12, 1978, 383.)Google Scholar
Kachanov, Yu. S., Kozlov, V. V. & Levchenko, V. Ya. 1978a Experiments on nonlinear interaction of waves in boundary layer. AIAA Paper, 78–1131. (See also Eppler & Fasel, 1980, p. 135.)
Kachanov, Yu. S., Kozlov, V. V. & Levchenko, V. Ya. 1978b Generation of Tollmien–Schlichting waves in a boundary layer at influence of external disturbances. Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza 5, 85 (in Russian).Google Scholar
Kachanov, Yu. S., Kozlov, V. V. & Levchenko, V. Ya. 1982 Beginning of Turbulence in a Boundary Layer. Novosibirsk: Nauka (in Russian).
Kachanov, Yu. S., Kozlov, V. V., Levchenko, V. Ya. & Ramazanov, M. P. 1984 Experimental study of K-regime of breakdown of laminar boundary layer. Preprint 9–84, Novosibirsk, ITPM SO AN SSSR (in Russian). (See also Kozlov, 1985, p. 61.)
Kachanov, Yu. S. & Levchenko, V. Ya. 1982 The resonant interaction of disturbances at laminar–turbulent transition in a boundary layer. Preprint 10–82, Novosibirsk, ITPM SO AN SSSR (in Russian). (See also J. Fluid Mech. 138, 1984, 209.)
Klebanoff, P. S. & Tidstrom, K. D. 1959 Evolution of amplified waves leading to transition in a boundary layer with zero pressure gradient. NACA Tech. Note D-195.
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12, 1.Google Scholar
Kleiser, L. 1982 Numerische Simulationen zum Laminar–Turbulenten Unschlagsprozess der ebenen Poiseuille-Stromung. Ph.D. dissertation, Inst. Reaktorentwicklung Kern Forschungs-zentrum Karlsruhe.
Kovasznay, L. S., Komoda, H. & Vasudeva, B. R. 1962 Detailed flow field in transition. In Proc. Heat Transfer and Fluid Mech. Inst., p. 1. Stanford University Press.
Kozlov, V. V. (ed.) 1985 Laminar–Turbulent Transition. Springer.
Kozlov, V. V. & Ramazanov, M. P. 1984 Formation of three-dimensional structures in Poiseuille flow at resonant interaction. Dokl. Akad. Nauk SSSR 275, 6 (in Russian).Google Scholar
Landahl, M. T. 1972 Wave mechanics of breakdown. J. Fluid Mech. 56, 775.Google Scholar
Laurien, E. 1986 Numerische Simulation zur aktiven Beeinflussung des laminar-turbulent Übergangs in der Plattengrenzschichtströmung. D.-Ing. dissertation, Institut für Theoretische Strömungsmechanik, DFVLR, Göttingen.
Miksad, R. W. 1973 Experiments of nonlinear interaction in the transition of a free shear layer. J. Fluid Mech. 59, 1.Google Scholar
Morkovin, M. V. 1968 Critical evaluation of transition from laminar to turbulent shear layer with emphasis of hypersonically travelling bodies. AFFDL Tech. Rep. 68–149.
Nayfeh, A. H. & Bozatli, A. N. 1979a Nonlinear wave interactions in boundary layers. AIAA Paper 79-1493.
Nayfeh, A. H. & Bozatli, A. N. 1979b Nonlinear of waves in boundary-layer flows. VPI & SU Rep. NVPI-E-79.6.
Nishioka, M., Asai, M. & Iida, S. 1980 An experimental investigation of the secondary instability. In Laminar–Turbulent Transition (ed. R. Eppler & H. Fasel), p. 37. Springer.
Orszag, S. A. & Patera, A. T. 1983 Secondary instability of wall-bounded shear flows. J. Fluid Mech. 128, 347–385.Google Scholar
Reatz, G. S. 1959 Northrop Rep. NOR-59, 383 (BLC-121). (See also Stuart, 1960.)
Saric, W. S., Carter, J. D. & Reynolds, G. A. 1981 Computation and visualization of unstable-wave streamlines in a boundary layer. Bull. Am. Phys. Soc. 26, 1252.Google Scholar
Saric, W. S., Kozlov, V. V. & Levchenko, V. Ya. 1984 Forced and unforced subharmonic resonance in boundary-layer transition. AIAA-84-0007.
Schubauer, G. B. & Klebanoff, P. S. 1956 Contribution on the mechanisms of boundary-layer transition. NACA Rep. 1289.
Schubauer, G. B. & Skramstad, H. K. 1947 Laminar boundary layer oscillations and stability of laminar flow. J. Aerospace Sci. 14, No. 2.Google Scholar
Stuart, J. T. 1960 Non-linear effects in hydrodynamic stability. In Proc. 10th Intl Congr. Appl. Mech., Stresa, Italy, pp. 91–97. Elsevier.
Thomas, A. S. W. & Saric, W. S. 1981 Harmonic and subharmonic waves during boundary-layer transition. Bull. Am. Phys. Soc. 26, 1252.Google Scholar
Volodin, A. G. & Zelman, M. B. 1978 Three-wave resonant interaction of disturbances in a boundary layer. Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza 5, 78 (in Russian).Google Scholar
Wray, A. & Hussaini, M. Y. 1984 Numerical experiments in boundary-layer stability. Proc. R. Soc. Lond. A 392, 373–389.Google Scholar
Zelman, M. B. 1981 A development of disturbances with finite amplitudes in plane flows. Preprint 10, Novosibirsk, ITPM SO AN SSSR (in Russian).Google Scholar
Zelman, M. B. & Maslennikova, I. I. 1982 Instability of sub- and supersonic flows (ed. V. Ya. Levchenko), pp. 5–15. Novosibirsk: ITPM SO AN SSSR (in Russian).
Zhigulyov, V. N., Krikinskiy, A. N., Sidorenko, N. V. & Tumin, A. M. 1976 On a mechanism of secondary instability and its role in a process of turbulence beginning. In Aerodynamics. Moscow: Nauka (in Russian).