Linear wave reflection by trench with various shapes |
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| Authors: | Tae-Hwa Jung Kyung-Duck Suh Seung Oh Lee Yong-Sik Cho |
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| Affiliation: | aDepartment of Civil Engineering, Hanyang University, Seoul 133-791, Korea;bDepartment of Civil and Environmental Engineering & Engineering Research Institute, Seoul National University, Seoul 151-744, Korea;cSchool of Urban & Civil Engineering, Hongik University, Seoul 121-791, Korea |
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| Abstract: | 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. The water depth inside the trench varies in proportion to a power of the distance from the center of the trench (which is the deepest water depth point and the origin of x-coordinate in this study). The mild-slope equation is transformed into a second-order ordinary differential equation with variable coefficients based on the longwave assumption [Hunt's, 1979. Direct solution of wave dispersion equation. Journal of Waterway, Port, Coast. and Ocean Engineering 105, 457–459] as approximate solution for wave dispersion. The analytical solutions are then obtained by using the power series technique. The analytical solutions are compared with the numerical solution of the hyperbolic mild-slope equations. After obtaining the analytical solutions under various conditions, the results are analyzed. |
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| Keywords: | Trench Analytical solution Mild-slope equation Bragg reflection |
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