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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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