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On the stability of the decelerating laminar boundary layer

Published online by Cambridge University Press:  20 April 2006

Mohamed Gad-El-Hak ,
Stephen H. Davis ,
J. Thomas Mcmurray  and
Steven A. Orszag
Mohamed Gad-El-Hak
Affiliation:
Flow Research Company, 21414 68th Avenue South, Kent, Washington 98032
Permanent address: Department of Engineering Science and Applied Mathematics, North-western University, Evanston, IL 60201.
Stephen H. Davis
Affiliation:
Flow Research Company, 21414 68th Avenue South, Kent, Washington 98032
Permanent address: Department of Engineering Science and Applied Mathematics, North-western University, Evanston, IL 60201.
J. Thomas Mcmurray
Affiliation:
Flow Research Company, 21414 68th Avenue South, Kent, Washington 98032
Permanent address: Department of Engineering Science and Applied Mathematics, North-western University, Evanston, IL 60201.
Steven A. Orszag
Affiliation:
Flow Research Company, 21414 68th Avenue South, Kent, Washington 98032
Permanent address: Department of Engineering Science and Applied Mathematics, North-western University, Evanston, IL 60201.
 Permanent address: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139.
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Abstract

The stability of a decelerating boundary-layer flow is investigated experimentally and numerically. Experimentally, a flat plate having a Blasius boundary layer is decelerated in an 18 m towing tank. The boundary layer becomes unstable to two-dimensional waves, which break down into three-dimensional patterns, hairpin vortices, and finally turbulent bursts when the vortices lift off the wall. The unsteady boundary-layer equations are solved numerically to generate instantaneous velocity profiles for a range of boundary and initial conditions. A quasi-steady approximation is invoked and the stability of local velocity profiles is determined by solving the Orr–Sommerfeld equation using Chebyshev matrix methods. Comparisons are made between the numerical predictions and the experimentally observed instabilities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 138 , January 1984 , pp. 297 - 323
Copyright
© 1984 Cambridge University Press

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