Phase manipulation and the harmonic components of ringing forces on a surface-piercing column

C. J. Fitzgerald, P. H. Taylor, R. Eatock Taylor, J. Grice, J. Zang

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A general phase-based harmonic separation method for the hydrodynamic loading on a fixed structure in water waves of moderate steepness is proposed. An existing method demonstrated in the experimental study described by Zang et al. (Zang et al. 2010 In Proc. Third Int. Conf. on Appl. of Phys. Modelling to Port and Coastal Protection. pp. 1–7.) achieves the separation of a total diffraction force into odd and even harmonics by controlling the phase of incident focused waves. Underlying this method is the assumption that the hydrodynamic force in focused waves possesses a Stokes-like structure. Under the same assumption, it is shown here how the harmonic separation method can be generalized, so that the first four sum harmonics can be separated by phase control and linear combinations of the resultant time-histories. The effectiveness of the method is demonstrated by comparisons of the Fourier transforms of the combined time-histories containing the harmonics of interest. The local wave elevations around the focus time are also visualized for the first three harmonics in order to reveal the local dynamics driving components within the wave force time-history.
Original languageEnglish
Article number20130847
Pages (from-to)1-21
Number of pages21
JournalProceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
Issue number2168
Early online date8 Aug 2014
Publication statusPublished - 8 Aug 2014
Event27th International Workshop on Water Wave and Floating Bodies - Copenhagen, UK United Kingdom
Duration: 22 Apr 201225 Apr 2012


  • nonlinear
  • hydrodynamics
  • diffraction
  • numerical simulation
  • ringing


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