Journal of Engineering Mathematics

, Volume 69, Issue 4, pp 385–400 | Cite as

An alternative analytical solution for water-wave motion over a submerged horizontal porous plate

  • Yong Liu
  • Yu-cheng Li


This study gives an alternative analytical solution for water-wave motion over an offshore submerged horizontal porous-plate breakwater in the context of linear potential theory. The matched-eigenfunction-expansions method is used to obtain the solution. The solution consists of a symmetric part and an antisymmetric part. The symmetric part is also the solution of wave reflection by a vertical solid wall with a submerged horizontal porous plate attached to it. In comparison with previous analytical solutions with respect to finite submerged horizontal porous plates, no complex water-wave dispersion relations are included in the present solution. Thus, the present solution is easier for numerical implementation. Numerical examples show that the convergence of the present solution is satisfactory. The results of the present solution also agree well with previous results by different analytical approaches, as well as previous numerical results by different boundary-element methods. The present solution can be easily extended to the case of multi-layer submerged horizontal porous plates, which may be more significant in practice for meeting different tide levels.


Alternative solution Eigenfunction expansion Horizontal porous plate Water wave 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.College of EngineeringOcean University of ChinaQingdaoChina
  2. 2.State Key Laboratory of Coastal and Offshore EngineeringDalian University of TechnologyDalianChina

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