Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-19T22:44:31.205Z Has data issue: false hasContentIssue false
  • English
  • Français

The growth of localized disturbances in a laminar boundary layer

Published online by Cambridge University Press:  28 March 2006

William O. Criminale  and
Leslie S. G. Kovasznay
William O. Criminale
Affiliation:
Department of Mechanics, The Johns Hopkins University, Baltimore
Leslie S. G. Kovasznay
Affiliation:
Department of Mechanics, The Johns Hopkins University, Baltimore Present address: Department of Mechanical Engineering, Princeton University, Princeton, New Jersey.
Get access Rights & Permissions [Opens in a new window]

Abstract

The classical theory of the instability of laminar flow predicts the growth (or decay) rate and phase velocity of two-dimensional small disturbance waves. In order to study the growth and dispersion of an originally localized spot-like disturbance, the initial disturbance is built up from all possible simple-harmonic waves. The propagation velocity and amplification rate for each vector wave-number then follows from the two-dimensional theory by Squire's generalization. The initial development can be solved explicitly by a power series in time, and the asymptotic behaviour is also predicted. For times between initial and final periods, exact numerical calculations have been made using an IBM 709 electronic computer. The role which localized disturbances can play in ultimate transition to turbulent motion is also indicated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 14 , Issue 1 , September 1962 , pp. 59 - 80
Copyright
© 1962 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

Benjamin, T. Brooke 1961 J. Fluid Mech. 10, 401.
Criminale, Jr. W. O. 1960 AGARD Report, no. 266, Paris.
Emmons, H. W. 1951 J. Aero. Sci. 18, 490.
Grohne D. 1954 ZAMM 35, 344.
Klebanoff, P. S. & Tidstrom, K. D. 1959 NASA TN D-195.
Kovasznay, L. S. G. 1960 Aeronautics and Astronautics. London: Pergamon.
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Schlichting, H. 1935 Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Neue Folge, Band I, 4.
Schubauer, G. B. & Skarmstad, H. K. 1948 NACA Rep. no. 909.
Schubauer, G. B. & Klebanoff, P. S. 1956 NACA Rep. no. 1289.
Shen, S. F. 1954 J. Aero. Sci. 21, 62.
Squire, H. B. 1933 Proc. Roy. Soc. A, 142, 621.
Watson, J. 1960 Proc. Roy. Soc. A, 254, 562.
Zatt, J. A. 1958 Numerische Beiträge zur Stabilitätstheorie der Grenschichten. Berlin: Springer-Verlag.