An Analytical Solution for Wave Transformation Over Axi-Symmetric Topography  

作　　者：CUONG San Sieu CHANG Jen-Yi TSAI Chia-Cheng CHOU Wan-Rong 

机构地区：[1]aInstitute of Oceanography,National Taiwan University,Taipei 10617,China [2]Tainan University of Technology,Tainan 71002,China [3]Department of Marine Environmental Engineering,National Kaohsiung University of Science and Technology,Kaohsiung 81164,China [4]Department of Marine Environment and Engineering,National Sun Yat-Sen University,Kaohsiung 80424,China [5]Department of Hydraulic and Ocean Engineering,National Cheng Kung University,Tainan 701,China

出　　处：《China Ocean Engineering》2019年第6期694-703,共10页中国海洋工程（英文版）

基　　金：financially supported by the Ministry of Science and Technology of Taiwan,China(Grant No.MOST 107-2221-E-992)

摘　　要：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.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 

分 类 号：TV13[水利工程—水力学及河流动力学]