Havelock wavemakers, Westergaard dams and the Rayleigh hypothesis
 P. A. Martin
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Water of constant finite depth fills a semiinfinite channel, with a wavemaker, W, at one end. The generation of smallamplitude gravity waves by harmonic oscillations of W leads to a linear boundaryvalue problem for a velocity potential, ϕ. For vertical, plane wavemakers, there is a theory due to Havelock in which ϕ is represented as a convergent series of eigenfunctions, with coefficients determined by the boundary condition on W. We show that the same representation (with different coefficients) can also be used for some wavemakers with other shapes; the allowable geometries and forcings are determined. This is a hydrodynamic analogue of the socalled Rayleigh hypothesis in the theory of gratings. Similar results obtain for the hydrodynamic loading of dams due to shortduration earthquakes.
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 Title
 Havelock wavemakers, Westergaard dams and the Rayleigh hypothesis
 Journal

Journal of Engineering Mathematics
Volume 26, Issue 2 , pp 267280
 Cover Date
 19920501
 DOI
 10.1007/BF00042723
 Print ISSN
 00220833
 Online ISSN
 15732703
 Publisher
 Kluwer Academic Publishers
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 Authors

 P. A. Martin ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of Manchester, M13 9PL, Manchester, England