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An Analytical Solution for Wave Transformation Over axi-symmetric topography

China Ocean Engineering 2019年第6期33卷 694-703页

作者： CUONG San Sieu CHANG Jen-Yi TSAI Chia-Cheng CHOU Wan-Rong aInstitute of Oceanography National Taiwan UniversityTaipei 10617China Tainan University of Technology Tainan 71002China Department of Marine Environmental Engineering National Kaohsiung University of Science and TechnologyKaohsiung 81164China Department of Marine Environment and Engineering National Sun Yat-Sen UniversityKaohsiung 80424China Department of Hydraulic and Ocean Engineering National Cheng Kung UniversityTainan 701China

The present study considers wave scattering phenomena around a cylindrical island mounted on a general axisymmetric topography or a general submerged truncated axi-symmetric shoal based on the mild-slope equation. The method of separation of variables and Taylor series expansion are invoked to find the approximate solution to the variable water depth region which varies proportionally to an arbitrary power of radial distance. Validations against the solutions for the combined wave refraction and diffraction around a cylindrical island mounted on a paraboloidal shoal of Liu et al. in 2004 and the scattering and trapping of wave energy by a submerged truncated paraboloidal shoal of Lin and Liu in 2007 show excellent agreements as the power of radial distance being equal to two. For the solutions of wave refraction and diffraction around a cylindrical island mounted on a shoal with depth proportionally to an arbitrary power of radial distance, good agreements with Zhai et al.’s(2013) solutions are demonstrated. Since the robustness of the assumption of a general axi-symmetric geometry based on an arbitrary power variability of the radial distance, the present solution can be very conveniently employed to investigate the effects of bottom topography on wave scattering and trapping patterns.

关键词： general axi-symmetric topography mild-slope equation submerged truncated shoal wave refraction wave diffraction

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