On Step Approximation for Roseau's Analytical Solution of Water Waves

Chia-Cheng Tsai, Tai-Wen Hsu and Yueh-Ting Lin

Mathematical Problems in Engineering, 2011, vol. 2011, 1-20

Abstract:

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.

Date: 2011
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2011/607196.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2011/607196.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:607196

DOI: 10.1155/2011/607196

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().