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On Step Approximation for Roseau's Analytical Solution of Water Waves
Joint Authors
Tsai, Chia-Cheng
Hsu, Tai-Wen
Lin, Yueh-Ting
Source
Mathematical Problems in Engineering
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-05-16
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
An indirect eigenfunction marching method (IEMM) is developed to provide step approximations for water wave problems.
The bottom profile is in terms of successive flat shelves separated by abrupt steps.
The marching conditions are represented by the horizontal velocities at the steps in the solution procedure.
The approximated wave field can be obtained by solving a system of linear equations with unknown coefficients which represents the horizontal velocities under a proper basis.
It is also demonstrated that this solution method can be exactly reduced to the transfer-matrix method (TM method) for a specific setting.
The combined scattering effects of a series of steps can be described by a single two-by-two transfer matrix for connecting the far-field behaviors of both sides for this method.
The solutions obtained by the IEMM are basically exact for water wave problems considering step-like bottoms.
Numerical simulations were performed to validate the present and commonly used methods.
Furthermore, it also shows that the solutions obtained by the IEMM converge very well to Roseau's analytical solutions for both mild and steep curved bottom profiles.
The present method improves the converges of the TM method for solving water wave scattering over steep bathymetry.
American Psychological Association (APA)
Tsai, Chia-Cheng& Hsu, Tai-Wen& Lin, Yueh-Ting. 2011. On Step Approximation for Roseau's Analytical Solution of Water Waves. Mathematical Problems in Engineering،Vol. 2011, no. 2011, pp.1-20.
https://search.emarefa.net/detail/BIM-484633
Modern Language Association (MLA)
Tsai, Chia-Cheng…[et al.]. On Step Approximation for Roseau's Analytical Solution of Water Waves. Mathematical Problems in Engineering No. 2011 (2011), pp.1-20.
https://search.emarefa.net/detail/BIM-484633
American Medical Association (AMA)
Tsai, Chia-Cheng& Hsu, Tai-Wen& Lin, Yueh-Ting. On Step Approximation for Roseau's Analytical Solution of Water Waves. Mathematical Problems in Engineering. 2011. Vol. 2011, no. 2011, pp.1-20.
https://search.emarefa.net/detail/BIM-484633
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-484633