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Nonlinear spatial equilibration of an externally excited instability wave in a free shear layer

Published online by Cambridge University Press:  26 April 2006

Lennart S. Hultgren
Lennart S. Hultgren
Affiliation:
National Aeronautics and Space Administration, Lewis Research Center, Cleveland, OH 44135, USA
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Abstract

A two-dimensional disturbance evolving from a strictly linear, finite-growth-rate instability wave with nonlinear effects first becoming important in the critical layer is considered. The analysis is carried out for a general weakly non-parallel mean flow using matched asymptotic expansions. The flow in the critical layer is governed by a nonlinear vorticity equation which includes a spatial-evolution term. As in Goldstein & Hultgren (1988), the critical layer ages into a quasi-equilibrium one and the initial exponential growth of the instability wave is converted into a weak algebraic growth during the roll-up process. This leads to a next stage of evolution where the instability-wave growth is simultaneously affected by mean-flow divergence and nonlinear critical-layer effects and is eventually converted to decay. Expansions for the various streamwise regions of the flow are combined into a single composite formula accounting for both shear-layer spreading and nonlinear critical-layer effects and good agreement with the experimental results of Thomas & Chu (1989), Freymuth (1966), and C.-M. Ho & Y. Zohar (1989, private communication) is demonstrated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 236 , March 1992 , pp. 635 - 664
Copyright
© 1992 Cambridge University Press

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