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Group dynamics and wave resonances in a narrow gap: modes and reduced group velocity

Published online by Cambridge University Press:  25 November 2019

Wenhua Zhao*
Affiliation:
Faculty of Engineering and Mathematical Sciences, The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia
P. H. Taylor
Affiliation:
Faculty of Engineering and Mathematical Sciences, The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia
H. A. Wolgamot
Affiliation:
Faculty of Engineering and Mathematical Sciences, The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia
B. Molin
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, IRPHE, 13013Marseille, France
R. Eatock Taylor
Affiliation:
Department of Engineering Science, University of Oxford, OxfordOX1 3PJ, UK
*
Email address for correspondence: wenhua.zhao@uwa.edu.au

Abstract

The spatial and temporal structure of the resonant fluid response in a narrow gap (the so-called gap resonance) between two identical fixed boxes is investigated experimentally. Transient wave groups are used to excite the gap resonance from different wave approach directions. This shows a strong beating pattern and a very long duration, reflecting that gap resonance is a multi-mode resonant and weakly damped phenomenon. For head sea excitation the linear transfer function of the $m=2$ gap mode is as significant as that of the $m=1$ mode. Gap resonance can be driven through different mechanisms, e.g. linear excitation and a nonlinear frequency-doubling process. Significant wave group structure is shown in the gap, and the group structure is more distinct in the case with frequency doubling, i.e. long wave, excitation. Then it is clearer visually that the groups originate at the end of the gap, propagate along the gap and are then partially reflected from the other end. The groups within the gap are very clear because the group velocity is close to constant for the first few gap resonance modes, and much smaller than that for free waves on the open sea. In contrast, the phase speed of waves in the gap is larger than that for free waves outside. Only in the limit of short waves do the group velocity and phase speed of the gap modes tend to those of deep-water free waves. The group and phase speeds from these experiments match well the theoretical forms given by Molin et al. (Appl. Ocean Res., vol. 24 (5), 2002, pp. 247–260), albeit for a slightly different box cross-sectional shape.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press

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