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Fluctuation of magnitude of wave loads for a long array of bottom-mounted cylinders

Published online by Cambridge University Press:  11 April 2019

Xiaohui Zeng Open the ORCID record for Xiaohui Zeng [Opens in a new window] ,
Fajun Yu ,
Min Shi  and
Qi Wang
Xiaohui Zeng*
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100049, China
Fajun Yu
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100049, China
Min Shi
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China
Qi Wang
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100049, China
*
†Email address for correspondence: [email protected]
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Abstract

For wave loads on cylinders constituting a long but finite array in the presence of incident waves, variations in the magnitude of the load with the non-dimensional wavenumber exhibit interesting features. Towering spikes and nearby secondary peaks (troughs) associated with trapped modes have been studied extensively. Larger non-trapped regions other than these two are termed Region III in this study. Studies of Region III are rare. We find that fluctuations in Region III are regular; the horizontal distance between two adjacent local maximum/minimum points, termed fluctuation spacing, is constant and does not change with non-dimensional wavenumbers. Fluctuation spacing is related only to the total number of cylinders in the array, identification serial number of the cylinder concerned and wave incidence angle. Based on the interaction theory and constructive/destructive interference, we demonstrate that the fluctuation characteristics can be predicted using simple analytical formulae. The formulae for predicting fluctuation spacing and the abscissae of every peak and trough in Region III are proposed. We reveal the intrinsic mechanism of the fluctuation phenomenon. When the diffraction waves emitted from the cylinders at the ends of the array and the cylinder concerned interfere constructively/destructively, peaks/troughs are formed. The fluctuation phenomenon in Region III is related to solutions of inhomogeneous equations. By contrast, spikes and secondary peaks are associated with solutions of the eigenvalue problem. This study of Region III complements existing understanding of the characteristics of the magnitude of wave load. The engineering significances of the results are discussed as well.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 868 , 10 June 2019 , pp. 244 - 285
Copyright
© 2019 Cambridge University Press 

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