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On singular and highly oscillatory properties of the Green function for ship motions

Chen, XB; Guo Xiong, WU; (2001) On singular and highly oscillatory properties of the Green function for ship motions. Journal of Fluid Mechanics , 445 pp. 77-91. 10.1017/s0022112001005481. Green open access

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Abstract

The Green function used for analysing ship motions in waves is the velocity potential due to a point source pulsating and advancing at a uniform forward speed. The behaviour of this function is investigated, in particular for the case when the source is located at or close to the free surface. In the far field, the Green function is represented by a single integral along one closed dispersion curve and two open dispersion curves. The single integral along the open dispersion curves is analysed based on the asymptotic expansion of a complex error function. The singular and highly oscillatory behaviour of the Green function is captured, which shows that the Green function oscillates with indefinitely increasing amplitude and indefinitely decreasing wavelength, when a field point approaches the track of the source point at the free surface. This sheds some light on the nature of the difficulties in the numerical methods used for predicting the motion of a ship advancing in waves.

Type: Article
Title: On singular and highly oscillatory properties of the Green function for ship motions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/s0022112001005481
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Mechanical Engineering
URI: https://discovery.ucl.ac.uk/id/eprint/11749
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