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The Quarterly Journal of Mechanics and Applied Mathematics 1979 32(2):125-133; doi:10.1093/qjmam/32.2.125
© 1979 by Oxford University Press
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ON SURFACE WAVES IN THE PRESENCE OF IMMERSED VERTICAL BOUNDARIES. II

P. F. RHODES-ROBINSON

( Department of Mathematics, Victoria University of Wellington New Zealand )

In this paper a reduction method is derived for dealing with surface waves in arbitrary regions of water of finite depth with immersed vertical boundaries, thus extending an established result for infinite depth. The solution of the original boundary-value problem is expressed in terms of the solutions of a pair of reduced boundary-value problems, which are found to be similar to those for infinite depth. A further modification is possible which allows for the influence of surface tension, extending in like manner the result of the preceding paper. The theory is applied to an unsolved problem.


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