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Numerical study of ribbon-induced transition in Blasius flow

Published online by Cambridge University Press:  21 April 2006

Philippe R. Spalart  and
Kyung-Soo Yang
Philippe R. Spalart
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
Kyung-Soo Yang
Affiliation:
Stanford University, Stanford, CA 94305, USA
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Abstract

The early three-dimensional stages of transition in the Blasius boundary layer are studied by numerical solution of the Navier-Stokes equations. A finite-amplitude two-dimensional wave and low-amplitude three-dimensional random disturbances are introduced. Rapid amplification of the three-dimensional components is observed and leads to transition. For intermediate amplitudes of the two-dimensional wave the breakdown is of subharmonic type, and the dominant spanwise wavenumber increases with the amplitude. For high amplitudes the energy of the fundamental mode is comparable to the energy of the subharmonic mode, but never dominates it; the breakdown is of mixed type. Visualizations, energy histories, and spectra are presented. The sensitivity of the results to various physical and numerical parameters is studied. The agreement with experimental and theoretical results is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 178 , May 1987 , pp. 345 - 365
Copyright
© 1987 Cambridge University Press

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References

Craik, A. D. D. 1971 Nonlinear resonant instability in boundary layers. J. Fluid Mech. 50, 393–413.Google Scholar
Gaster, M. 1962 A note on the relationship between temporally increasing and spatially increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14, 222–224.Google Scholar
Herbert, Th. 1984 Analysis of the subharmonic route to transition. AIAA 84–0009.Google Scholar
Herbert, Th. 1985 Three-dimensional phenomena in the transitional flat-plate boundary layer. AIAA-85–0489.Google Scholar
Kachanov, Y. S. & Levchenko, V. Y. 1984 The resonant interaction of disturbances at laminar—turbulent transition in a boundary layer. J. Fluid Mech. 138, 209–247.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary layer instability. J. Fluid Mech. 12, 1–34.Google Scholar
Kleiser, L. & Laurien, E. 1985 Three-dimensional numerical simulation of laminar—turbulent transition and its control by periodic disturbances. In Laminar—Turbulent Transition, Proc. 2nd IUTAM Symp., Novosibirsk (ed. V. V. Kozlov), Springer.
Kovasznay, L. S. G., Komoda, H. & Vasudeva, B. R. 1962 Detailed flow field in transition. In Proc. 1962 Heat transfer and Fluid Mechanics Institute, pp. 1–26. Stanford University Press.
Laurien, E. & Kleiser, L. 1985 Active control of Tollmien—Schlichting waves in the Blasius boundary layer by periodic wall suction. In Proc. 6th GAMM Conf. on Numerical Methods in Fluid Dynamics, Göttingen, Sept. 25–27, 1985. Vieweg.
Orszag, S. A. & Kells, L. C. 1980 Transition to turbulence in plane Poiseuille and plane Couette flow. J. Fluid Mech. 96, 159–205.Google Scholar
Saric, W. S., Kozlov, V. V. & Levchenko, V. Y. 1984 Forced and unforced subharmonic resonance in boundary-layer transition. AIAA 84–0007.Google Scholar
Schlichting, H. 1979 Boundary layer theory, 7th edn. McGraw-Hill.
Spalart, P. R. 1984 Numerical simulation of boundary-layer transition 9th Intl Conf. on Numerical Methods in Fluid Dynamics, Paris, June 25–29, 1984 (ed. S. Soubbaramayer & J. P. Boujot), pp. 531–535. Springer.
Spalart, P. R. 1986 Numerical simulation of boundary layers: Part 1. Weak formulation and numerical method. NASA T. M. 88222.Google Scholar
Thomas, A. S. W. 1983 The control of boundary-layer transition using a wave-superposition principle. J. Fluid Mech. 137, 233–250.Google Scholar
Wray, A. & Hussaini, M. Y. 1980 Numerical experiments in boundary-layer stability. AIAA paper 80–0275 (see also Proc. R. Soc. Lond. A 392, 373–389).Google Scholar
Zang, T. A. & Hussaini, M. Y. 1985a Numerical experiments on subcritical transition mechanisms. AIAA 85–0296.Google Scholar
Zang, T. A. & Hussaini, M. Y. 1985b Numerical experiments on the stability of controlled shear flows. AIAA 85–1698.Google Scholar