Abstract
This study deals with a 3-D boundary-value problem that arises when free-surface waves interact with a stationary body or body system in a channel or wave tank of rectangular cross-section. A consistent asymptotic analysis and an efficient numerical solution is presented of the Green function that satisfies the linear free- surface condition and the non-penetration condition on the channel bottom and the sidewalls. The formulation is based on the open-sea Green function and the complete series of images is evaluated accurately based on the asymptotic analysis. It is demonstrated that the Green function has a square-root singular behavior due to the sidewalls when the wave frequency approaches one of the resonant frequencies. The numerical results for the Green function presented in this paper are believed to have an absolute accuracy of 10−5.
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Xia, J. Evaluation of the Green function for 3-D wave-body interactions in a channel. Journal of Engineering Mathematics 40, 1–16 (2001). https://doi.org/10.1023/A:1017533115478
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DOI: https://doi.org/10.1023/A:1017533115478