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The evolution of a localized disturbance in a laminar boundary layer. Part 2. Strong disturbances

Published online by Cambridge University Press:  26 April 2006

Kenneth S. Breuer  and
Marten T. Landahl
Kenneth S. Breuer
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Present address: Center for Fluid Mechanics, Turbulence and Computation, Box 1966, Brown University, Providence, RI 02912, USA.
Marten T. Landahl
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

Navier–Stokes calculations were performed to simulate the evolution of a moderate-amplitude localized disturbance in a laminar flat-plate boundary layer. It was found that, in accordance with previous results for linear and weakly nonlinear disturbances, the evolving disturbance consists of two parts: an advective, or transient portion which travels at approximately the local mean velocity, and a dispersive wave portion which grows or decays according to Tollmien–Schlichting instability theory. The advective portion grows much more rapidly than the wave portion, initially linearly in time and, in contrast to the weak-disturbance case, gives rise to two distinct nonlinear effects. The first is a streamwise growth of the disturbed region producing a low-speed streak, bounded in the vertical and spanwise directions by intense shear layers. The second nonlinear effect is the onset of a secondary instability on the vertical shear layer formed as a result of spanwise stretching of the mean vorticity and giving rise to oscillations in the v- and w-components with a substantially smaller spatial scale than that of the initial disturbance. The effect of initial spanwise scale is assessed by calculating the disturbance for three different cases in which the spanwise scale and the initial disturbance amplitude were varied. It was found that the resulting perturbation depends primarily on the initial distribution of v in each plane z = const., but is approximately independent of the spanwise scale.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 220 , November 1990 , pp. 595 - 621
Copyright
© 1990 Cambridge University Press

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References

Blackwelder, R. F.: 1983 Analogies between transitional and turbulent boundary layers. Phys. Fluids. 26, 2807–2815.Google Scholar
Breuer, K. S.: 1988 The development of a localized disturbance in a boundary layer. PhD thesis, Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, Cambridge, Mass.
Breuer, K. S. & Haritonidis, J. H., 1990 The evolution of a localized disturbance in a laminar boundary layer. Part 1. Weak disturbances. J. Fluid Mech. 220, 569–594.Google Scholar
Breuer, K. S., Landahl, M. T. & Spalart, P. R., 1987 The simulation of coherent structures in a laminar boundary layer. In Proc. 1987 Summer Program, Stanford/NASA Center for Turbulence Research.
Case, K. M.: 1960 Stability of inviscid plane Couette flow. Phys. Fluids. 3, 143–148.Google Scholar
Gaster, M.: 1975 A theoretical model for the development of a wave packet in a laminar boundary layer. Proc. R. Soc. Lond. A 347, 271–289.Google Scholar
Gaster, M. & Grant, I., 1975 An experimental investigation of the formation and development of a wave packet in a laminar boundary layer. Proc. R. Soc. Lond. A 347, 253–269.Google Scholar
Gustavsson, L. H.: 1978 On the evolution of disturbances in boundary layer flows. Trita-Mek-78-02. Department of Mechanics, Royal Institute of Technology, Stockholm.
Henningson, D. S.: 1988 The inviscid initial value problem for a piecewise linear mean flow. Stud. Appl. Maths 78, 31–56.Google Scholar
Henningson, D. S., Johansson, A. V. & Lundbladh, A., 1989 On the evolution of localized disturbances in laminar shear flows. In Proc. Third IUTAM Symposium on Laminar–Turbulent transition, Toulouse. (To be published by Springer.)
Henningson, D. S., Spalart, P. & Kim, J., 1987 Numerical simulations for turbulent spots in plane Poiseuille and boundary layer flows. Phys. Fluids. 30, 2914–2917.Google Scholar
Johansson, A. V., Alfredsson, P. H. & Kim, J., 1987 Shear layer structure in near wall turbulence. In Proc. 1987 Summer Program, pp. 237–251. NASA/Stanford Center for Turbulence Research.
Johansson, A. V., Her, J. & Haritonidis, J. H., 1987 On the generation of high amplitude wall-pressure peaks in turbulent boundary layers and spots. J. Fluid Mech. 175, 119–142.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
Kovasznay, L. S. G., Komoda, H. & Vasudeva, B. R., 1962 Detailed flow field in transition. In Proc. 1962 Heat Transfer and Fluid Mechanics Institute, Stanford University, pp. 1–26.Google Scholar
Landahl, M. T.: 1975 Wave breakdown and turbulence. SIAM J. Appl. Maths 28, 735–756.Google Scholar
Landahl, M. T.: 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243–251.Google Scholar
Landahl, M. T.: 1990 On sublayer streaks. J. Fluid Mech. 212, 593–614.Google Scholar
Landahl, M. T., Breuer, K. S. & Haritonidis, J. H. Dec. 1987 Transients and waves in boundary layer transition. In Nonlinear Wave Interactions in Fluids, pp. 17–21. Boston, MA: ASME.
Morkovin, M. V.: 1969 The many faces of transition. In Viscous Drag Reduction (ed. C. Wells). Plenum.
Orszag, S. A. & Patera, A. T., 1983 Secondary instability of wall-bounded shear flows. J. Fluid Mech. 128, 347–385.Google Scholar
Spalart, P. R.: 1986 Numerical simulation of boundary layers: Part 1. Weak formulation and numerical method. NASA TM 88222.Google Scholar
Spalart, P. R.: 1988 Direct simulation of a turbulent boundary layer up to Re0 = 1410. J. Fluid Mech. 187, 61–98.Google Scholar
Spalart, P. R. & Yang, K., 1987 Numerical study of ribbon induced transition in blasius flow. J. Fluid Mech. 178, 345–365.Google Scholar
Stuart, J. T.: 1960 On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows. I. The basic behavior in plane Poiseuille flow. J. Fluid Mech. 9, 353.Google Scholar
Stuart, J. T.: 1965 The production of intense shear layers by vortex stretching and convection. AGARD Rep. 514.Google Scholar
Swearingen, J. D. & Blackwelder, R. F., 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 255–290.Google Scholar
Wray, A. & Hussaini, M. Y., 1984 Numerical experiments in boundary layer stability. Proc. R. Soc. Lond. A 392, 373–389.Google Scholar