A low-order theory for stability of non-parallel boundary layer flows

Govindarajan, R and Narasimha, R (1997) A low-order theory for stability of non-parallel boundary layer flows. In: Proceedings Of The Royal Society Of London Series A-Mathematical Physical And Engineering Sciences, 453 (1967). pp. 2537-2549.

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Abstract

Abstract: As a sequel to the earlier analysis of Govindarajan & Narasimha, we formulate here the lowest-order rational asymptotic theory capable of handling the linear stability of spatially developing two-dimensional boundary layers. It is shown that a new ordinary differential equation, using similarity-transformed variables in Falkner-Skan flows, provides such a theory correct upto (but not including) O(R-2/3), where R is the local boundary layer thickness Reynolds number. The equation so derived differs from the Orr-Sommerfeld in two respects: the terms representing streamwise diffusion of vorticity are absent; but a new term for the advection of disturbance vorticity at the critical layer by the mean wall-normal velocity was found necessary. Results from the present lowest-order theory show reasonable agreement with the full O(R-1) theory. Stability loops at different wall-normal distances, in either theory, show certain peculiar characteristics that have not been reported so far but are demonstrated here to be necessary consequences of flow non-parallelism.

Item Type:	Journal Article
Publication:	Proceedings Of The Royal Society Of London Series A-Mathematical Physical And Engineering Sciences
Publisher:	Royal Society
Additional Information:	Copyright of this article belongs to Royal Society.
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	10 Feb 2010 07:14
Last Modified:	19 Sep 2010 05:00
URI:	http://eprints.iisc.ac.in/id/eprint/18269

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