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Waves Generated by Shear Layer Instabilities

Morland, L. C. and Saffman, P. G. and Yuen, H. C. (1991) Waves Generated by Shear Layer Instabilities. Proceedings of the Royal Society of London. Series A, Mathematical, Physical and Engineering Sciences, 433 (1888). pp. 441-450. ISSN 0962-8444.

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Stern & Adam and subsequent workers have considered the linear stability of two-dimensional, parallel, ideal fluid flow with shear in the presence of a free surface. In these studies a fluid current is modelled as a finite layer of constant vorticity above a semi-infinite stagnant region, corresponding to a piecewise-linear velocity profile. Here, an investigation of the stability of currents for several smooth velocity profiles is presented. With surface tension present it is found that the fluid surface velocity must still exceed the minimum wavespeed of stagnant fluid for instability to occur; a result highlighted by Caponi et al. for piecewise-linear profiles. Instability growth rates are found to be significantly smaller than those associated with a piecewise-linear profile. There are also qualitative differences in the stability characteristics; in particular, transition is associated with an exchange of stability for smooth profiles, but not for the piecewise-linear profile.

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Additional Information:© 1991 The Royal Society. Received 26 November 1990; accepted 10 January 1991. We thank Dr S. Cowley for many helpful discussions and in particular his advice concerning the numerics. Partial financial support by the Office of Naval Research (Grant N000-14-89-J-1164) is gratefully acknowledged.
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Office of Naval Research (ONR)N000-14-89-J-1164
Issue or Number:1888
Record Number:CaltechAUTHORS:20141217-134302177
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Official Citation:Waves Generated by Shear Layer Instabilities L. C. Morland, P. G. Saffman and H. C. Yuen Proceedings: Mathematical and Physical Sciences Vol. 433, No. 1888 (May 8, 1991) , pp. 441-450 Published by: The Royal Society Stable URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:52970
Deposited By: Tony Diaz
Deposited On:17 Dec 2014 22:41
Last Modified:03 Oct 2019 07:46

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