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Gap resonance and higher harmonics driven by focused transient wave groups

Published online by Cambridge University Press:  09 January 2017

W. Zhao Open the ORCID record for W. Zhao [Opens in a new window] ,
H. A. Wolgamot ,
P. H. Taylor  and
R. Eatock Taylor
W. Zhao*
Affiliation:
Faculty of Engineering, Computing and Mathematics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
H. A. Wolgamot
Affiliation:
Faculty of Engineering, Computing and Mathematics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
P. H. Taylor
Affiliation:
Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
R. Eatock Taylor
Affiliation:
Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
*
†Email address for correspondence: [email protected]
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Abstract

The first and higher harmonic components of the resonant fluid response in the gap between two identical fixed rectangular boxes are experimentally investigated in a wave basin. Gap response is excited by transient wave groups (being based on scaled versions of the autocorrelation function of sea-state spectra, representing NewWaves, the average shape of large waves in a sea state). Several different wave groups with different maximum surface elevations, spectral peak frequencies and bandwidths are used, while the bilge shape of the boxes and approach angle of the waves are also varied. Unlike a simple regular wave, it is complicated to separate the harmonic components for a transient wave group due to nonlinear wave–wave and wave–structure interactions. A four-phase combination methodology is used to separate the first four harmonic components, and this also allows higher harmonic components to be isolated with simple digital frequency filtering. Harmonic components up to 14th order in the incident wave amplitude have been extracted. It is shown that for an incident group with appropriate frequency content, the linear gap response may be substantially smaller than the second harmonic component, which is strongly driven via quadratic coupling of the linear terms from the incident wave and occurs in the gap resonant modes. Double frequency excitation may have important practical implications for offshore operations. Fourth and zeroth (long-wave) harmonics in the gap are further driven via quadratic coupling of the second harmonic itself. Linear damping coefficients for the first few modes of the gap resonant response are derived from measured time series using a numerical fit and shown to be higher than those from linear diffraction calculations.

JFM classification

Waves/Free-surface Flows: Wave scattering Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 905 - 939
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Copyright
© 2017 Cambridge University Press 

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Zhao et al. supplementary movie

Movie 1 (for Set I) shows the recorded free surface motions at the 7 wave gauges within the gap and the two just outside the gap at each end as circle markers - they are joined by spline interpolation. Also shown is a dotted blue line which represents the free surface in the absence of the boxes. Note that the focus time is t=0.

Download Zhao et al. supplementary movie(Video)
Video 3.8 MB

Zhao et al. supplementary movie

Movie 2 was recorded by a video camera placed within one of the boxes during Set I, and shows the free surface in the gap around the location of WG4 (in fact WG4 may be seen in the gap).

Download Zhao et al. supplementary movie(Video)
Video 5 MB

Zhao et al. supplementary movie

Similar as in Movie 1 but without incident free surface elevations

Download Zhao et al. supplementary movie(Video)
Video 2.9 MB

Zhao et al. supplementary movie

The same as in Movie 1 but for Set VIB

Download Zhao et al. supplementary movie(Video)
Video 3.5 MB