Journal ArticleDOI
An analytical solution of the mild-slope equation for waves around a circular island on a paraboloidal shoal
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TLDR
In this article, an analytical technique in terms of series expansions was developed to solve the mild-slope equation on an axi-symmetric topography, which is applied to study the combined refraction and diffraction of plane monochromatic waves by a circular cylindrical island mounted on a paraboloidal shoal.About:
This article is published in Coastal Engineering.The article was published on 2004-08-01. It has received 50 citations till now. The article focuses on the topics: Mild-slope equation & Fourier series.read more
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Linear Wave Reflection by Trench with Various Shapes
TL;DR: In this paper, two types of analytical solutions for waves propagating over an asymmetric trench are derived, one is a long wave solution and the other is a mild-slope solution, which is applicable to deeper water.
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Analytical study of Bragg resonance by singly periodic sinusoidal ripples based on the modified mild-slope equation
TL;DR: In this article, the wave propagation over singly periodic sinusoidal ripples is studied analytically based on the modified mild-slope equation (MMSE), where each ripple region is divided into four monotonic subintervals such that there is only one regular singular point of the MMSE within each subinterval which is located at one of the two endpoints.
Journal ArticleDOI
Scattering and Trapping of Wave Energy by a Submerged Truncated Paraboloidal Shoal
TL;DR: In this paper, Liu et al. studied the scattering and trapping of wave energy by a submerged truncated paraboloidal shoal, where the mild-slope equation was transformed into an explicit equation by using Hunt's 1979 Pade approximation to the wave dispersion equation.
Journal ArticleDOI
An analytic solution to the mild slope equation for waves propagating over an axi-symmetric pit
Tae-Hwa Jung,Kyung-Duck Suh +1 more
TL;DR: In this paper, an analytic solution to the mild slope equation is derived for waves propagating over an axi-symmetric pit located in an otherwise constant depth region, where the water depth inside the pit decreases in proportion to an integer power of radial distance from the pit center.
Journal ArticleDOI
An exact analytic solution to the modified mild-slope equation for waves propagating over a trench with various shapes
Jian-Jian Xie,Huan-Wen Liu +1 more
TL;DR: An exact analytic solution to the modified mild-slope equation (MMSE) in terms of Taylor series for waves propagating over an asymmetrical trench with various shapes is given in this paper.
References
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Journal ArticleDOI
Computation of Combined Refraction — Diffraction
TL;DR: In this paper, the derivation of a two-dimensional differential equation, which describes the phenomenon of combined refraction - diffraction for simple harmonic waves, and a method of solving this equation is presented.
Journal ArticleDOI
A new approach to free vibration analysis using boundary elements
TL;DR: In this article, a boundary element method for the analysis of free vibrations in solid mechanics is developed using a non-standard boundary integral approach, utilizing the statical fundamental solution and employing a special class of coordinate functions, the algebraic eigenvalue problem results.
Wave forces on piles: a diffraction theory
R. C. MacCamy,R. A. Fuchs +1 more
TL;DR: In this paper, a quantitative understanding of the forces developed by wave action against circular piling is presented, where the authors focus on the effect of wave action on circular piling and show that wave action is a powerful force against piling.
Journal ArticleDOI
Diffraction and refraction of surface waves using finite and infinite elements
Peter Bettess,O. C. Zienkiewicz +1 more
TL;DR: In this article, the wave problem is introduced and a derivation of Berkhoff's surface wave theory is outlined, and appropriate boundary conditions are described, for finite and infinite boundaries.
Journal ArticleDOI
The modified mild-slope equation
P. G. Chamberlain,D. Porter +1 more
TL;DR: A modified version of the mild-slope equation is derived and its predictions of wave scattering by two-dimensional topography compared with those of other equations and with experimental data.