Author

# W. R. Dean

Bio: W. R. Dean is an academic researcher. The author has contributed to research in topics: Surface wave & Vertical plane. The author has an hindex of 2, co-authored 2 publications receiving 452 citations.

Topics: Surface wave, Vertical plane, Wind wave, Plane (geometry), Cylinder

##### Papers

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01 Jul 1947

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.

299 citations

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01 Jan 1950

TL;DR: In this article, a method for the calculation of surface waves of small amplitude generated on deep water by a normal velocity distribution of period 2π/σ prescribed over a submerged circular cylinder is given.

Abstract: A method is given for the calculation of the surface waves of small amplitude generated on deep water by a normal velocity distribution of period 2π/σ prescribed over a submerged circular cylinder. The method of solution involves a system of linear equations in an infinite number of unknowns; this system always possesses a solution. The unknowns may be obtained as power series in a parameter Ka, convergent for sufficiently small values of the parameter. When the parameter is not small, the equations can be solved by infinite determinants. It is shown that the reflexion coefficient of waves incident on a fixed circular cylinder vanishes, as was first shown by Dean. The pulsations of a submerged cylinder are discussed when the normal velocity is the same at all points of the cylinder at any given time.

180 citations

##### Cited by

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TL;DR: A surface plasmon polariton (SPP) is an electromagnetic excitation existing on the surface of a good metal, whose electromagnetic field decays exponentially with distance from the surface.

Abstract: A surface plasmon polariton (SPP) is an electromagnetic excitation existing on the surface of a good metal. It is an intrinsically two-dimensional excitation whose electromagnetic field decays exponentially with distance from the surface. In the past, it was possible to study only the (far-field) scattered light produced by the interaction of surface polaritons with surface features. Only with the development of scanning near-field optical microscopy did it become possible to measure the surface polariton field directly in close proximity to the surface where the SPP exists. Here we overview the near-field studies of surface polaritons on randomly rough and nanostructured surfaces, theoretical models of SPP interaction with surface features, and SPP applications in novel photonic technologies. Surface polariton scattering, interference, backscattering, and localization will be discussed, as well as concepts of surface polariton optics and polaritonic crystals. Surface polaritons are finding an ever increasing number of applications in traditional domains of surface characterization and sensors as well as in newly emerging nano-photonic and optoelectronic technologies.

2,211 citations

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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

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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

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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

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343 citations