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On waves at an interface between two liquids

Published online by Cambridge University Press:  24 October 2008

P. F. Rhodes-Robinson
Affiliation:
Department of Mathematics, Victoria University of Wellington, New Zealand

Abstract

In this paper it is shown that a class of linearized interface-wave problems for two superposed inviscid liquids of unequal densities occupying regions which are symmetric about the interface can be reduced to a surface-wave problem in the lower region together with a classical hydrodynamical problem for potential flow in the lower region under a plane lid. The effect of interfacial tension is included. Examples of fundamental singularities in two semi-infinite liquids are given.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

REFERENCES

(1)Gorgui, M. A.Wave motion due to a cylinder heaving at the surface separating two infinite liquids. J. Nat. Sci. Math. 16 (1977), 120.Google Scholar
(2)Gorgui, M. A. and Kassem, S. E.Basic singularities in the theory of internal waves. Quart. J. Mech. Appl. Math. 31 (1978), 3148.Google Scholar
(3)Gorgui, M. A. and Kassem, S. E.On the generation of short internal waves by cylinders oscillating at the surface separating two infinite liquids. Math. Proc. Cambridge Philos. Soc. 83 (1978), 481494.Google Scholar
(4)Lamb, H.Hydrodynamics, 6th ed. (Cambridge, 1932).Google Scholar
(5)Rhodes-Robinson, P. F.On the forced surface waves due to a vertical wave-maker in the presence of surface tension. Proc. Cambridge Philos. Soc. 70 (1971), 323337.Google Scholar
(6)Wehausen, J. V. Free surface flows. Research Frontiers in Fluid Dynamics (1965), 534640 (Interscience).Google Scholar
(7)Wehausen, J. V. and Laitone, E. V. Surface waves. Handbuch der Physik 9 (1960), 446778 (Springer).Google Scholar