On the forced surface waves due to a partially immersed vertical wave-maker in water of infinite depth

Author:
P. F. Rhodes-Robinson

Journal:
Quart. Appl. Math. **54** (1996), 709-719

MSC:
Primary 76B15

DOI:
https://doi.org/10.1090/qam/1417234

MathSciNet review:
MR1417234

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Abstract: In this paper we determine the velocity potential describing the two-dimensional antisymmetric wave motion generated by a harmonically oscillating vertical plane wave-maker partially immersed in water of infinite depth. The solution of the boundary-value problem for the velocity potential is obtained from a formulation depending on the unknown horizontal velocity on the line of antisymmetry below the wave-maker, which leads to a singular integral equation of known type for a related reduction variable. The idea was developed by Ursell to solve the corresponding transmission problem and another rigid wave-maker problem, and uses classical wave-maker theory.

**[1]**D. V. Evans,*A note on the waves produced by the small oscillations of a partially immersed vertical plate*, J. Inst. Math. Appl.**17**, 135-140 (1976)**[2]**M. D. Haskind,*The radiation and diffraction of surface waves from a vertically floating plate*, Prikl. Mat. Meh.**23**, 546-556 (1959) (Russian), translated as J. Appl. Math. Mech.**23**, 770-783 (1960)**[3]**T. H. Havelock,*Forced surface waves on water*, Philos. Mag.**8**, 569-576 (1929)**[4]**M. Lewin,*The effect of vertical barriers on progressing waves*, J. Math. and Phys.**42**, 287-300 (1963)**[5]**F. Ursell,*The effect of a fixed vertical barrier on surface waves in deep water*, Proc. Cambridge Philos. Soc.**43**, 374-382 (1947)**[6]**F. Ursell,*On the waves due to the rolling of a ship*, Quart. J. Mech. Appl. Math.**1**, 246-252 (1948)

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DOI:
https://doi.org/10.1090/qam/1417234

Article copyright:
© Copyright 1996
American Mathematical Society