# The effect of a fixed vertical barrier on surface waves in deep water

01 Jul 1947-Vol. 43, Iss: 3, pp 374-382

TL;DR: In this paper, it was shown that when the normal velocity is prescribed at each point of an infinite vertical plane extending from the surface, the motion on each side of the plane is completely determined.

Abstract: In this paper the two-dimensional reflection of surface waves from a vertical barrier in deep water is studied theoretically.It can be shown that when the normal velocity is prescribed at each point of an infinite vertical plane extending from the surface, the motion on each side of the plane is completely determined, apart from a motion consisting of simple standing waves. In the cases considered here the normal velocity is prescribed on a part of the vertical plane and is taken to be unknown elsewhere. From the condition of continuity of the motion above and below the barrier an integral equation for the normal velocity can be derived, which is of a simple type, in the case of deep water. We begin by considering in detail the reflection from a fixed vertical barrier extending from depth a to some point above the mean surface.

##### Citations

More filters

[...]

TL;DR: In this paper, the evanescent field structure over the wave front, as represented by equiphase planes, is identified as one of the most important and easily recognizable forms of surface wave.

Abstract: This paper calls attention to some of the most important and easily recognizable forms of surface wave, pointing out that their essential common characteristic is the evanescent field structure over the wave front, as represented by equiphase planes. The problems of launching and supporting surface waves must, in general, be distinguished from one another and it does not necessarily follow that because a particular surface is capable of supporting a surface wave that a given aperture distribution of radiation, e.g. a vertical dipole, can excite such a wave. The paper concludes with a discussion of the behavior of surface waves and their applications.

1,244 citations

•

15 Jan 1957

TL;DR: In this article, two-dimensional waves on a running stream in water of uniform depth were modeled as a moving pressure point, and the theory of the wave pattern created by a moving ship was proposed.

Abstract: Basic Hydrodynamics. The Two Basic Approximate Theories. WAVES SIMPLE HARMONIC IN THE TIME. Simple Harmonic Oscillations in Water of Constant Depth. Waves Maintained by Simple Harmonic Surface Pressure in Water of Uniform Depth: Forced Oscillations. Waves on Sloping Beaches and Past Obstacles. MOTIONS STARTING FROM REST: TRANSIENTS. Unsteady Motions. WAVES ON A RUNNING STREAM: SHIP WAVES. Two-Dimensional Waves on a Running Stream in Water of Uniform Depth. Waves Caused by a Moving Pressure Point: Kelvin's Theory of the Wave Pattern Created by a Moving Ship. The Motion of a Ship, as a Floating Rigid Body, in a Seaway. Long Waves in Shallow Water. Mathematical Hydraulics. Problems in Which Free Surface Conditions Are Satisfied Exactly: The Breaking of a Dam Levi-Civita's Theory. Bibliography. Indexes.

980 citations

••

TL;DR: In this article, the authors consider the case of a ship lying dead in the water and assume that the body does not disturb the water much during its forward motion, for example, slenderness or thinness.

Abstract: We shall restrict ourselves here to floating bodies without any means of propelling themselves. The body may, of course, be a ship lying dead in the water, but there is no real limitation to practical shapes of any particular sort except that we shall suppose the body to be hydrostatically stable. This will restrict the extent of this survey in an important way: we are able to slough off all effects associated with an average velocity of the body. Since mathematical solution of problems almost inevitably proceeds by way of linearization of the boundary conditions, this means that we may avoid introducing a linearization parameter whose smallness expresses the fact that the body doesn't disturb the water much during its forward motion, for example, slenderness or thinness. If we do introduce such a geometrical assumption, it will be an additional approximation, not one forced upon us by the physical situation. Fortunately, Newman's (1970) article treats, among other things, the recent advances in the theory of motion of slender ships under way. More can be found in a paper by Ogilvie (1964) . We shall assume from the beginning that motions are small and take this into account in formulating equations and boundary conditions. Further more, we shaH assume the fluid inviscid, and without surface tension. It is not difficult to write down equations and boundary conditions for a less restricted problem. However, since most results are for the case of small motions and since the perturbation expansions associated with the deriva tion of the linearized problem from the more exact one do not present any special points of interest, it seems more efficient to start with the simpler problem. Even so, some account will be given of recent attempts to consider nonlinear problems.

419 citations

••

343 citations

••

TL;DR: In this paper, the scattering of infinitesimal surface waves normally incident on a rectangular obstacle in a channel of finite depth is considered and a variational formulation is used as the basis of numerical computations.

Abstract: The scattering of infinitesimal surface waves normally incident on a rectangular obstacle in a channel of finite depth is considered. A variational formulation is used as the basis of numerical computations. Scattering properties for bottom and surface obstacles of various proportions, including thin barriers and surface docks, are presented. Comparison with experimental and theoretical results by other investigators is also made.

291 citations

##### References

More filters

••

01 Nov 1945

TL;DR: In this paper, the reflexion of waves on the surface of water by a thin plane vertical barrier is considered and the coefficient of reflexion (the ratio of the amplitudes, at a great distance from the barrier, of the reflected and incident waves) is calculated.

Abstract: 1. The reflexion of waves on the surface of water by a thin plane vertical barrier is considered and the coefficient of reflexion (the ratio of the amplitudes, at a great distance from the barrier, of the reflected and incident waves) is calculated. If the top edge is at a depth a below the surface, it is found that the coefficient of reflexion is about ¼ when where T is the period of the incident waves, so that the condition that the coefficient may exceed ¼ is a .

118 citations