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Finite-Amplitude Waves in Inviscid Shear Flows

Moore, D. W. and Saffman, P. G. (1982) Finite-Amplitude Waves in Inviscid Shear Flows. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 382 (1783). pp. 389-410. ISSN 1364-5021. http://resolver.caltech.edu/CaltechAUTHORS:20150128-125338803

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Abstract

This paper examines the existence and properties of steady finite-amplitude waves of cats-eye form superposed on a unidirectional inviscid, incompressible shear flow. The problem is formulated as the solution of nonlinear Poisson equations for the stream function with boundary conditions on the unknown edges of the cats-eyes. The dependence of vorticity on stream function is assumed outside the cats-eyes to be as in the undisturbed flow, and uniform unknown vorticity is assumed inside. It is argued on the basis of a finite difference discretization that the problem is determinate, and numerical solutions are obtained for Couette-Poiseuille channel flow. These are compared with the predictions of a weakly nonlinear theory based on the approach of Benney & Bergeron (1969) and Davis (1969). The phase speed of the waves is found to be linear in the wave amplitude.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1098/rspa.1982.0108DOIArticle
http://rspa.royalsocietypublishing.org/content/382/1783/389PublisherArticle
http://www.jstor.org/stable/2397401JSTORArticle
Additional Information:© 1982 The Royal Society. This work was supported by the Office of Naval Research and the Department of Energy (Office of Basic Energy Sciences). We wish to thank Control Data Corporation for the grant of time on the Cyber 203 at the C.D.C. Service Center, Arden Hills, Minnesota. We also wish to thank Dr J. C. Schatzman for a great deal of help and for preparing the graphic output of figure 6. The authors are grateful to Professor J. T. Stuart, F.R.S., for some valuable comments.
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Office of Naval Research (ONR)UNSPECIFIED
Department of Energy (DOE)UNSPECIFIED
Record Number:CaltechAUTHORS:20150128-125338803
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150128-125338803
Official Citation:Moore, D. W., & Saffman, P. G. (1982). Finite-Amplitude Waves in Inviscid Shear Flows. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 382(1783), 389-410. doi: 10.2307/2397401
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ID Code:54188
Collection:CaltechAUTHORS
Deposited By: Joanne McCole
Deposited On:28 Jan 2015 23:20
Last Modified:28 Jan 2015 23:20

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