Journal of Engineering Mathematics

, Volume 114, Issue 1, pp 115–129 | Cite as

Boundary-integral representations for ship motions in regular waves

  • Jiayi He
  • Yi Zhu
  • Huiyu Wu
  • Chen-Jun Yang
  • Wei Li
  • Francis NoblesseEmail author


Alternative boundary-integral representations of linear potential flow around a ship that travels at a constant speed in regular (time-harmonic) waves in deep water are considered. In particular, the Neumann–Michell (NM) boundary-integral representation of steady flow around a ship traveling in calm water is extended to ship motions in regular waves. This extension is straightforward, but points to a complicated and unresolved fundamental issue that is essentially related to the formulation of a linear flow model. Indeed, the NM boundary-integral flow representation for ship motions in regular waves given in the study suggests that the classical Neumann–Kelvin (NK) flow model may be inadequate at a ship waterline. Alternative NM boundary-integral representations of time-harmonic ship waves that are consistent with the previously given NM representation of ship waves in calm water, and yield Fourier–Kochin representations of ship waves that are well suited for numerical computations, are given.


Frequency-domain approach Neumann–Kelvin theory Neumann–Michell theory Potential flow Ship motions 



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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean & Civil Engineering, Collaborative Innovation Center for Advanced Ship and Deep-Sea ExplorationShanghai Jiao Tong UniversityShanghaiChina

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