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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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References

Bennetts, L. G., Peter, M. A. & Montiel, F. 2017 Localisation of Rayleigh–Bloch waves and damping of resonant loads on arrays of vertical cylinders. J. Fluid Mech. 813, 508–527.Google Scholar
Callan, M., Linton, C. M. & Evans, D. V. 1991 Trapped modes in two-dimensional waveguides. J. Fluid Mech. 229, 51–64.Google Scholar
Evans, D. V., Levitin, M. & Vassiliev, D. 1994 Existence theorems for trapped modes. J. Fluid Mech. 261, 21–31.Google Scholar
Evans, D. V. & Porter, R. 1998 Trapped modes embedded in the continuous spectrum. Q. J. Mech. Appl. Maths 52 (2), 263–274.Google Scholar
Evans, D. V. & Porter, R. 1999 Trapping and near-trapping by arrays of cylinders in waves. J. Engng Maths 35, 149–179.Google Scholar
Goo, J. S. & Yoshida, K. 1990 A numerical method for huge semisubmersible responses in waves. SNAME Trans. 98, 365–387.Google Scholar
Kagemoto, H. & Yue, D. K. P. 1986 Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J. Fluid Mech. 166, 189–209.Google Scholar
Kashiwagi, M. 2000 Hydrodynamic interactions among a great number of columns supporting a very large flexible structure. J. Fluids Struct. 14, 1013–1034.Google Scholar
Kashiwagi, M. 2017 Hydrodynamic interactions of multiple bodies with water waves. Intl J. Offshore Polar Engng 27, 113–122.Google Scholar
Linton, C. M. & Evans, D. V. 1990 The interaction of waves with arrays of vertical circular cylinders. J. Fluid Mech. 215, 549–569.Google Scholar
Linton, C. M. & Evans, D. V. 1992a Integral equations for a class of problems concerning obstacles in waveguides. J. Fluid Mech. 245, 349–365.Google Scholar
Linton, C. M. & Evans, D. V. 1992b The radiation and scattering of surface waves by a vertical circular cylinder in a channel. Phil. Trans. R. Soc. Lond. 338, 325–357.Google Scholar
Linton, C. M. & Evans, D. V. 1993 The interaction of waves with a row of circular cylinders. J. Fluid Mech. 251, 687–708.Google Scholar
Linton, C. M. & McIver, M. 2002a Periodic structures in waveguides. Proc. R. Soc. Lond. A 458, 3003–3021.Google Scholar
Linton, C. M. & McIver, M. 2002b The existence of Rayleigh–Bloch surface waves. J. Fluid Mech. 470, 85–90.Google Scholar
Linton, C. M., McIver, M., McIver, P., Ratcliffe, K. & Zhang, J. 2002 Trapped modes for off-centre structures in guides. Wave Motion 36 (1), 67–85.Google Scholar
Linton, C. M., Porter, R. & Thompson, I. 2007 Scattering by a semi-infinite periodic array and the excitation of surface waves. SIAM J. Appl. Maths 67 (5), 1233–1258.Google Scholar
Linton, C. M. & Thompson, I. 2007 Resonant effects in scattering by periodic arrays. Wave Motion 44, 165–175.Google Scholar
Maniar, H. D. & Newman, J. N. 1997 Wave diffraction by a long array of cylinders. J. Fluid Mech. 339, 309–330.Google Scholar
McIver, P. & Evans, D. V. 1984 Approximation of wave forces on cylinder arrays. Appl. Ocean Res. 6 (2), 101–107.Google Scholar
Montiel, F., Squire, V. & Bennetts, L. 2015 Evolution of directional wave spectra through finite regular and randomly perturbed arrays of scatterers. SIAM J. Appl. Maths 75 (2), 630–651.Google Scholar
Montiel, F., Squire, V. & Bennetts, L. 2016 Attenuation and directional spreading of ocean wave spectra in the marginal ice zone. J. Fluid Mech. 790, 492–522.Google Scholar
Newman, J. N. 1997 Resonant diffraction problems. In Proceedings 12th International Workshop on Water Waves and Floating Bodies (Carry le Rouet, France), pp. 307–308. IWWWFB.Google Scholar
Newman, J. N. 2017 Trapped-wave modes of bodies in channels. J. Fluid Mech. 812, 178–198.Google Scholar
Peter, M. A. & Meylan, M. H. 2007 Water-wave scattering by a semi-infinite periodic array of arbitrary bodies. J. Fluid Mech. 575, 473–494.Google Scholar
Peter, M. A., Meylan, M. H. & Linton, C. M. 2006 Water-wave scattering by a periodic array of arbitrary bodies. J. Fluid Mech. 548, 237–256.Google Scholar
Porter, R. & Evans, D. V. 1999 Rayleigh–Bloch surface waves along periodic gratings and their connection with trapped modes in waveguides. J. Fluid Mech. 386, 233–258.Google Scholar
Simon, M. J. 1982 Multiple scattering in arrays of axisymmetric wave-energy devices. Part 1. A matrix method using a plane-wave approximation. J. Fluid Mech. 120, 1–25.Google Scholar
Spring, B. H. & Monkmeyer, P. L. 1974 Interaction of plane waves with vertical cylinders. In Proceedings 14th International Conference on Coastal Engineering (Copenhagen, Denmark), pp. 1828–1847. ASCE.Google Scholar
Thomas, G. P. 1991 The diffraction of water waves by a circular cylinder in a channel. Ocean Engng 18 (1/2), 17–44.Google Scholar
Thompson, I., Linton, C. M. & Porter, R. 2008 A new approximation method for scattering by long finite arrays. Q. J. Mech. Appl. Maths 61 (3), 333–352.Google Scholar
Utsunomiya, T. & Eatock Taylor, R. 1999 Trapped modes around a row of circular cylinders in a channel. J. Fluid Mech. 386, 259–279.Google Scholar
Walker, D. A. G. & Eatock Taylor, R. 2005 Wave diffraction from linear arrays of cylinders. Ocean Engng 32, 2053–2078.Google Scholar