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.
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)
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)
T. H. Havelock, Forced surface waves on water, Philos. Mag. 8, 569–576 (1929)
M. Lewin, The effect of vertical barriers on progressing waves, J. Math. and Phys. 42, 287–300 (1963)
F. Ursell, The effect of a fixed vertical barrier on surface waves in deep water, Proc. Cambridge Philos. Soc. 43, 374–382 (1947)
F. Ursell, On the waves due to the rolling of a ship, Quart. J. Mech. Appl. Math. 1, 246–252 (1948)
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)
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)
T. H. Havelock, Forced surface waves on water, Philos. Mag. 8, 569–576 (1929)
M. Lewin, The effect of vertical barriers on progressing waves, J. Math. and Phys. 42, 287–300 (1963)
F. Ursell, The effect of a fixed vertical barrier on surface waves in deep water, Proc. Cambridge Philos. Soc. 43, 374–382 (1947)
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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Article copyright:
© Copyright 1996
American Mathematical Society