, Volume 26, Issue 2, pp 267-280

Havelock wavemakers, Westergaard dams and the Rayleigh hypothesis

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Abstract

Water of constant finite depth fills a semi-infinite channel, with a wavemaker, W, at one end. The generation of small-amplitude gravity waves by harmonic oscillations of W leads to a linear boundary-value 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 so-called Rayleigh hypothesis in the theory of gratings. Similar results obtain for the hydrodynamic loading of dams due to short-duration earthquakes.