A Caltech Library Service

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. doi:10.1098/rspa.1982.0108.

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item:


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
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.
Funding AgencyGrant Number
Office of Naval Research (ONR)UNSPECIFIED
Department of Energy (DOE)UNSPECIFIED
Issue or Number:1783
Record Number:CaltechAUTHORS:20150128-125338803
Persistent URL:
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
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54188
Deposited On:28 Jan 2015 23:20
Last Modified:10 Nov 2021 20:30

Repository Staff Only: item control page