Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.coastaleng.2004.04.005
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dc.titleAn analytical solution of the mild-slope equation for waves around a circular island on a paraboloidal shoal
dc.contributor.authorLiu, H.-W.
dc.contributor.authorLin, P.
dc.contributor.authorShankar, N.J.
dc.date.accessioned2014-06-17T08:13:08Z
dc.date.available2014-06-17T08:13:08Z
dc.date.issued2004-08
dc.identifier.citationLiu, H.-W., Lin, P., Shankar, N.J. (2004-08). An analytical solution of the mild-slope equation for waves around a circular island on a paraboloidal shoal. Coastal Engineering 51 (5-6) : 421-437. ScholarBank@NUS Repository. https://doi.org/10.1016/j.coastaleng.2004.04.005
dc.identifier.issn03783839
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/65111
dc.description.abstractIn this paper, we develop an analytical technique in terms of series expansions to solve the mild-slope equation on an axi-symmetric topography. This technique is applied to study the combined refraction and diffraction of plane monochromatic waves by a circular cylindrical island mounted on a paraboloidal shoal. By using the direct solution for the wave dispersion equation by Hunt [J. Waterw., Port, Coast., Ocean Div. Proc ASCE 4 (1979) 457], the mild-slope equation becomes explicit and it is then solved in terms of combined Fourier series and Taylor series. It is found that, to calculate the wave elevation along a perimeter with a specific radius, more terms in the Taylor series and angular modes in the Fourier series are needed for shorter waves. On the other hand, for the same incident wave, the outer the solutions are sought, more angular modes are needed to obtain the converged result of Fourier series. The comparison with the analytical solution based on the linear shallow-water equation by Homma [Geophys. Mag. 21 (1950) 199] is made for long wave incidence and excellent agreements are obtained. For long waves and waves in intermediate water depth, comparisons are made with other numerical results of the mild-slope equation and an equally good quality of agreement is achieved. © 2004 Elsevier B.V. All rights reserved.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1016/j.coastaleng.2004.04.005
dc.sourceScopus
dc.subjectAnalytical solution
dc.subjectHomma's island
dc.subjectThe mild-slope equation
dc.subjectWave diffraction
dc.subjectWave dispersion
dc.subjectWave refraction
dc.typeArticle
dc.contributor.departmentCIVIL ENGINEERING
dc.description.doi10.1016/j.coastaleng.2004.04.005
dc.description.sourcetitleCoastal Engineering
dc.description.volume51
dc.description.issue5-6
dc.description.page421-437
dc.description.codenCOEND
dc.identifier.isiut000223902500007
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