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

Govindarajan, Rama and Narasimha, R (1997) A low-order theory for stability of non-parallel boundary layer flows. Proceedings of the Royal Society of London, Series A (Mathematical, Physical and Engineering Sciences), 453 (1967). pp. 2537-2549. ISSN 1364-5021

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Abstract

As a sequel to the earlier analysis of Govindarajan amp;amp; Narasimha (1996), 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(Rlt;supgt;-2/3lt;/supgt;), 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(Rlt;supgt;-1lt;/supgt;) 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
Uncontrolled Keywords: Boundary layers;Differential equations;Diffusion;Flow instability;Vortices;Low-order theory;Nonparallel boundary layer flows
Subjects: ENGINEERING > Fluid Mechanics and Thermodynamics
Division/Department: Computational and Theoretical Fluid Dynamics Division, Computational and Theoretical Fluid Dynamics Division
Depositing User: MS Jayashree S
Date Deposited: 19 Apr 2007
Last Modified: 24 May 2010 09:55
URI: http://nal-ir.nal.res.in/id/eprint/4139

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