Journal ArticleDOI

# Oblique surface-wave diffraction by a cylindrical obstacle

01 Dec 1981-Dynamics of Atmospheres and Oceans (Elsevier)-Vol. 6, Iss: 2, pp 121-123
TL;DR: In this paper, the diffraction of a surface wave that is obliquely incident upon a small cylindrical deformation of the bottom of a laterally unbounded ocean is calculated by small perturbation theory.
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TL;DR: The linear theory for water waves impinging obliquely on a vertically sided porous structure is examined in this article, where the reflection and transmission coefficients are significantly altered and they are calculated using a plane-wave assumption.
Abstract: The linear theory for water waves impinging obliquely on a vertically sided porous structure is examined. For normal wave incidence, the reflection and transmission from a porous breakwater has been studied many times using eigenfunction expansions in the water region in front of the structure, within the porous medium, and behind the structure in the down-wave water region. For oblique wave incidence, the reflection and transmission coefficients are significantly altered and they are calculated here. Using a plane-wave assumption, which involves neglecting the evanescent eigenmodes that exist near the structure boundaries (to satisfy matching conditions), the problem can be reduced from a matrix problem to one which is analytic. The plane-wave approximation provides an adequate solution for the case where the damping within the structure is not too great. An important parameter in this problem is Γ 2 = ω 2 h ( s - i f )/ g , where ω is the wave angular frequency, h the constant water depth, g the acceleration due to gravity, and s and f are parameters describing the porous medium. As the friction in the porous medium, f , becomes non-zero, the eigenfunctions differ from those in the fluid regions, largely owing to the change in the modal wavenumbers, which depend on Γ 2 . For an infinite number of values of ΓF 2 , there are no eigenfunction expansions in the porous medium, owing to the coalescence of two of the wavenumbers. These cases are shown to result in a non-separable mathematical problem and the appropriate wave modes are determined. As the two wavenumbers approach the critical value of Γ 2 , it is shown that the wave modes can swap their identity.

260 citations

Journal ArticleDOI
TL;DR: In this paper, two time-dependent equations for wave propagation on rapidly varying topography are developed using different theoretical approaches and are shown to be identical for random and monochromatic wave propagation.

119 citations

Journal ArticleDOI
Hsien-Kuo Chang
TL;DR: In this paper, the reflection and transmission of long waves from a trapezoid breakwater and a series of trapezoidal breakwaters, using the matching method, was analyzed. But the results of the analysis were limited to the case of a single breakwater, and the top plane width and the arrangement of the breakwaters were not the major parameters in designing multiply composite Bragg breakwaters.

72 citations

### Cites background or methods from "Oblique surface-wave diffraction by..."

• ...Wave reflection from sets of different numbers of breakwaters, using the proposed method and Miles method. H.-K. Chang, J.-C. Liou / Ocean Engineering 34 (2007) 185–191 189...

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• ...The expressions for reflection and transmission coefficients derived by Miles (1981) are written as RMiles ¼ 2k2 2khþ sinh 2kh Z 1 1 dðxÞe2ikxdx (16) and TMiles ¼ 1þ i 2k2 2khþ sinh 2kh Z 1 1 dðxÞdx , (17) where d(x) is the shape function of the obstacle of which the height is measured from the…...

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• ...The shoaling effect yields a transmission coefficient of greater than unity. present method, Mei (1983) and Miles (1981) ARTICLE IN PRESS H.-K. Chang, J.-C. Liou / Ocean Engineering 34 (2007) 185–191 189 If the slope of the sloping face varies, but the width of the top plane is fixed, then the…...

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• ...Section 4.1 compares the wave ARTICLE IN PRESS H.-K. Chang, J.-C. Liou / Ocean Engineering 34 (2007) 185–191186 reflections obtained by the method herein with those obtained by Mei (1983) and Miles (1981)....

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• ...The proposed method incorporates the conservations of both energy flux and mass, yielding more reasonable reflections than those obtained by Miles’ (1981) method....

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DOI
20 May 1991
TL;DR: In this paper, the authors consider the Bragg reflection of surface waves by parallel bars placed discretely on the seabed and consider the application of resonant interaction theory to the dominant Fourier mode of the bar field.
Abstract: We consider the extension of previous theories for Bragg reflection of surface waves by parallel bars to the case of artificial bars placed discretely on the seabed. The case of non-resonant, weak reflection is considered first, followed by a consideration of the application of resonant interaction theory to the dominant Fourier mode of the bar field. Both theories are compared to numerical results, and discrepancies are seen in both cases. Finally, experimental results are compared to theory.

49 citations

Journal ArticleDOI
TL;DR: In this paper, the problem of scattering of obliquely incident surface water waves by small undulation on a sea-bed is considered for solution by assuming that the bed is composed of porous material of a specific type.

49 citations

### Cites background or result from "Oblique surface-wave diffraction by..."

• ..., when G ′ = 0, the results (21) and (22) agree with the ones obtained by Miles [9], Mandal and Basu [5] (for the case of absence of surface tension) and Martha and Bora [6]....

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• ...Mandal and Basu [5] generalized the problem of Miles [9] to include the effect of surface tension at the free surface....

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• ...(22) For the special case with negligible porosity of the sea-bed, i.e., when G ′ = 0, the results (21) and (22) agree with the ones obtained by Miles [9], Mandal and Basu [5] (for the case of absence of surface tension) and Martha and Bora [6]....

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• ...Miles [9] and Davies and Heathershaw [3] considered the problem of water-wave scattering by a sea-bed with an undulating bottom topography....

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##### References
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01 Jul 1958
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

Book
30 Nov 1971
TL;DR: In this paper, an intermediate-level text on the use of integral transforms in applied mathematics and engineering is presented, which is divided into five parts covering integral transform pairs, the Laplace transform, Fourier transforms, Hankel transform, and finite Fourier transform.
Abstract: An intermediate-level text on the use of integral transforms in applied mathematics and engineering. Existing works either cover the subject in more elementary form or are advanced treatises. In a very lucid style the author deals with the use of this important mathematical tool to solve ordinary and partial differential equations in problems in electrical circuits, mechanical vibration and wave motion, heat conduction, and fluid mechanics. The book is divided into five parts covering integral transform pairs, the Laplace transform, Fourier transforms, Hankel transforms, and finite Fourier transforms. A basic knowledge of complex variables and elementary differential equations is assumed. There are many exercises and examples drawn from the above fields, tables of the transform pairs needed in the text, and a glossary of terms with which the student may be unfamiliar. For the student who seeks further background on the subject, an annotated bibliography is provided.

44 citations