Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-25T04:16:41.386Z Has data issue: false hasContentIssue false

Multipole expansions for two superposed fluids, each of finite depth

Published online by Cambridge University Press:  24 October 2008

S. E. Kassem
Affiliation:
Department of Mathematics, Faculty of Science, Moharrem Bey, Alexandria, Egypt

Abstract

Problems dealing with the generation of internal waves at the surface separating two fluids involves the consideration of different types of singularities in one of the two fluids. In this paper the velocity potentials describing line and point multipoles are obtained for the case when each fluid is of finite constant depth, neglecting effects of surface tension at the surface of separation.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Gourgi, M. A. and Kasseh, S. E.Basic singularities in the theory of internal waves. Quart. J. Mech. Appl. Math. 31 (1978), 3148.Google Scholar
(2)Rhodes-Robinson, P. F.Fundamental singularities in the theory of water waves with surface tension. Butt. Austral. Math. Soc. 2 (1970), 317333.Google Scholar
(3)Thorne, R. C.Multipole expansions in the theory of surface waves. Proc. Cambridge Philos. Soc. 49 (1953), 707716.CrossRefGoogle Scholar
(4)Ursell, F.Surface waves on deep water in the presence of a submerged circular cylinder. I. Proc. Cambridge Philos. Soc. 46 (1950), 141152.CrossRefGoogle Scholar