# The cylindrical wave‐maker problem in water of uniform finite depth in the presence of surface tension

01 May 1991-International Journal of Mathematical Education in Science and Technology (Taylor & Francis Group)-Vol. 22, Iss: 3, pp 429-433

TL;DR: In this paper, the classical vertical cylindrical wave-maker problem in water of finite depth under the influence of surface tension is investigated by employing a suitable Weber transform in the radial coordinate.

Abstract: In the present note the classical vertical cylindrical wave‐maker problem in water of finite depth under the influence of surface tension is reinvestigated by employing a suitable Weber transform in the radial coordinate.

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01 Sep 1971TL;DR: In this article, the boundary-value problem for the velocity potential of a wave-maker is solved for both infinite and finite constant depth, and the solution of the corresponding problem concerning the axisymmetric wave motion due to a vertical cylindrical wavemaker is deduced in conclusion.

Abstract: The classical wave-maker problem to determine the forced two-dimensional wave motion with outgoing surface waves at infinity generated by a harmonically oscillating vertical plane wave-maker immersed in water was solved long ago by Sir Thomas Havelock. In this paper we reinvestigate the problem, making allowance for the presence of surface tension which was excluded before, and obtain a solution of the boundary-value problem for the velocity potential which is made unique by prescribing the free surface slope at the wave-maker. The cases of both infinite and finite constant depth are treated, and it is essential to employ a method which is new to this problem since the theory of Havelock cannot be extended in the latter case of finite depth. The solution of the corresponding problem concerning the axisymmetric wave motion due to a vertical cylindrical wave-maker is deduced in conclusion.

61 citations

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TL;DR: In this paper, the Fourier cosine integral transform in the horizontal co-ordinate was used to obtain the amplitude of the wave at large distances from the wavemaker. But the amplitude was not obtained in a natural manner.

8 citations

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TL;DR: In this paper, the Laplace transform in time and Weber transform in the radial co-ordinate were used to obtain the velocity potential and hence the inertial surface depression for a vertical circular cylindrical wavemaker immersed in a liquid.

4 citations