Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-18T23:18:39.406Z Has data issue: false hasContentIssue false
  • English
  • Français

The evolution of a localized disturbance in a laminar boundary layer. Part 1. Weak disturbances

Published online by Cambridge University Press:  26 April 2006

Kenneth S. Breuer  and
Joseph H. Haritonidis
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, Providency, RI 02912, USA.
Joseph H. Haritonidis
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The evolution of a low-amplitude localized disturbance in a laminar boundary layer is considered. Linear inviscid theory illustrates that the disturbance may be divided into two parts: a dispersive wave part, represented by solutions to the Rayleigh equation which travel at their characteristic speeds, and a transient or advective part travelling at the local mean velocity. For a three-dimensional initial disturbance, calculations based on linear inviscid theory indicate that the transient portion of the disturbance does not decay and has the form of an inclined shear layer which elongates as the disturbance propagates downstream. The amplitude of the transient part exceeds by far that of the wave part of the disturbance. Experimental results are presented for a disturbance created by the impulsive motion of a small membrane flush-mounted at the wall. For small amplitudes, the initial evolution of the disturbance is found to be in good qualitative agreement with the inviscid calculations, showing the rapid formation of an inclined shear layer. Further downstream, the transient portion of the disturbance decays owing to viscous effects, leaving a linearly unstable dispersive wave packet. The evolutions of equal and opposite disturbances are compared and it is shown that, despite a weak nonlinearity that develops, the resultant wave packets are equal in structure but of opposite phase.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 220 , November 1990 , pp. 569 - 594
Copyright
© 1990 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Amini, J. & Lespinard, G., 1982 Experimental study of an ‘incipient spot’ in a transitional boundary layer. Phys. Fluids 25, 1743–1750.Google Scholar
Antar, B. N. & Benek, J. A., 1978 Temporal eigenvalue spectrum of the Orr–Sommerfeld equations for the Blasius boundary layer. Phys. Fluids 21, 183–189.Google Scholar
Benney, D. J. & Gustavsson, L. H., 1981 A new mechanism for linear and nonlinear hydrodynamic instability. Stud. Appl. Maths 64, 185–209.Google Scholar
Breuer, K. S., Haritonidis, J. H. & Landahl, M. T., 1989 The control of localized disturbances in a boundary layer through active wall motion. Phys. Fluids 3, 574–582.Google Scholar
Breuer, K. S. & Landahl, M. T., 1990 The evolution of a localized disturbance in a laminar boundary layer. Part 2. Strong disturbances. J. Fluid Mech. 220, 595–621.Google Scholar
Case, K. M.: 1960 Stability of inviscid plane Couette flow. Phys. Fluids 3, 143–148.Google Scholar
Cohen, J., Breuer, K. S. & Haritonidis, J. H., 1990 On the evolution of a wave packet in a laminar boundary layer. J. Fluid Mech. (submitted).Google Scholar
Craik, A. D. D.: 1971 Nonlinear resonant instability in boundary layers. J. Fluid Mech. 50, 393–413.Google Scholar
Diprima, R. C. & Habetler, G. J., 1969 A completeness theorem for non-selfadjoint eigenvalue problems in hydrodynamic stability. Arch. Rat. Mech. Anal. 32, 218.Google Scholar
Drazin, P. G. & Reid, W. H., 1981 Hydrodynamic Stability. Cambridge University Press.
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
Gresko, L. S.: 1988 Characteristics of wall pressure and near-wall velocity in a flat plate turbulent boundary layer. FDRL Rep. 88–2. Department of Aeronautics and Astronautics, Massachusetts Institute of Technology.
Grosch, C. E. & Salwen, H., 1978 The continuous spectrum of the Orr–Sommerfeld equation. Part 1. The spectrum and the eigenfunctions. J. Fluid Mech. 87, 33–54.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
Herbert, T.: 1984 Analysis of the subharmonic route to transition in boundary layers. AIAA 84–0009.Google Scholar
Jordinson, R.: 1970 The flat plate boundary layer. Part 1. Numerical integration of the Orr–Sommerfeld equation. J. Fluid Mech. 43, 801–811.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.: 1984 Coherent structures in turbulence and Prandtl's mixing length theory. Z. Flugwiss. Weltraumforsch. 8, 233–242.Google Scholar
Lin, C. C.: 1955 Theory of Hydrodynamic Stability. Cambridge University Press.
Lueptow, R., Breuer, K. S. & Haritonidis, J. H., 1988 Computer-aided x-wire calibration using a look-up table. Expts Fluids 6, 115–118.Google Scholar
Mack, L. M.: 1976 A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer. J. Fluid Mech. 73, 497–520.Google Scholar
Mangus, J. F.: 1984 Preliminary measurements of drag and bursting frequency in a manipulated turbulent boundary layer. FDRL Rep. 84–2. Department of Aeronautics and Astronautics, Massachusetts Institute of Technology.
Orr, W. M. F.: 1907 The stability of the steady motions of a perfect liquid and of a viscous liquid. Part I: A perfect liquid. Part II: A viscous liquid. Proc. R. Irish Acad. A 27, 9–138.Google Scholar
Orszag, S. A. & Patera, A. T., 1983 Secondary instability of wall-bounded shear flows. J. Fluid Mech. 128, 347–385.Google Scholar
Russell, J. M. & Landahl, M. T., 1984 The evolution of a flat eddy near a wall in an inviscid shear flow. Phys. Fluids 27, 557–570.Google Scholar
Stuart, J. T.: 1965 The production of intense shear layers by vortex stretching and convection. AGARD Rep. 514.Google Scholar