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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
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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

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