Journal of Marine Science and Application

, Volume 17, Issue 3, pp 371–379 | Cite as

Viscous-Flow-Based Analysis of Wave Near-Trapped in a Four-Cylinder Structure

  • Zhengke Wang
  • Guanghua HeEmail author
  • Zhigang Zhang
  • Yanghan Meng
Research Article


The hydrodynamic analysis of multi-floating bodies is important and widely used in marine engineering. In this study, we systematically simulated the wave diffraction problem of a fixed vertical four-cylinder structure in regular waves in the time domain in a viscous numerical wave tank. The hydrodynamic interaction of waves with a bottom-mounted structure consisting of four vertical cylinders arranged at the corners of a square shows a complicated interference phenomenon. In this paper, we illustrate and analyze the run-up around the structure and the corresponding wave forces. To investigate the viscous effect on the near-trapping phenomenon, we pay particular attention to investigating the waves near-trapped inside the four-cylinder structure, and make a comparative study of the viscous- and inviscid-flow solutions with the experimental measurements. The results show that the maximum wave elevation occurs on the inner side of the leeside cylinder, and that the wave elevations on the outer side of the cylinders are lower than those on the inner side. We can conclude that viscosity has an obvious damping effect on wave elevations inside the structure. The cylinders show a tendency to drift apart from each other when the near-trapping phenomenon occurs.


Cylinder Near-trapping Viscous flow Wave elevations Regular waves 


  1. Ansys Fluent Inc (2014) Ansys Fluent 15.0 Theory GuideGoogle Scholar
  2. Bai W, Feng X, Taylor RE, Ang KK (2014) Fully nonlinear analysis of near-trapping phenomenon around an array of cylinders. Appl Ocean Res 44(3):71–81. CrossRefGoogle Scholar
  3. Cao HJ, Wan DC (2017) Benchmark computations of wave run-up on single cylinder and four cylinders by naoe-FOAM-SJTU solver. Appl Ocean Res 65:327–337. CrossRefGoogle Scholar
  4. Chen JT, Lee YT, Lin YJ (2009) Interaction of water waves with vertical cylinders using null-field integral equations. Appl Ocean Res 31(2):101–110. CrossRefGoogle Scholar
  5. Chen JT, Wu CF, Chen IL, Lee JW (2012) On near-trapped modes and fictitious frequencies for water wave problems containing an array of circular cylinders using a null-field boundary integral equation. Eur J Mech 32(5):32–44. MathSciNetCrossRefzbMATHGoogle Scholar
  6. Cong PW, Gou Y, Teng B, Zhang K, Huang YF (2015) Model experiments on wave elevation around a four-cylinder structure. Ocean Eng 96:40–55. CrossRefGoogle Scholar
  7. Evans DV, Porter R (1997) Near-trapping of waves by circular arrays of vertical cylinders. Appl Ocean Res 19(2):83–99. CrossRefGoogle Scholar
  8. Evans DV, Porter R (1999) Trapping and near-trapping by arrays of cylinders in waves. J Eng Math 35(1–2):149–179. MathSciNetCrossRefzbMATHGoogle Scholar
  9. He GH, Chen LM, Wang DZ (2016) FINE/marine-based numerical simulation of forward-speed radiation problems of a Wigley hull. J Harbin Eng Univ 37(10):1335–1340. (in Chinese).
  10. He GH, Zhang ZH, Wang ZK, Qi C (2018) Time-domain simulation of large-amplitude motion and green water loading of Wigley hull. J Harbin Eng Univ 39(8):1269–1277. (in Chinese).
  11. He GH, Zhang ZG, Zhang ZH, Zhang SJ (2017) Reduction in wave drift force on marine structures by cloaking phenomenon. J Harbin Eng Univ 38(11):1676–1681. (in Chinese).
  12. Jiang SC, Lv L, Teng B, Gou Y (2011) Hydrodynamic analyses for near-trapping of a four-cylinder structure under water waves. J Harbin Eng Univ 32(5):546–554. (in Chinese).
  13. Kagemoto H, Murai M, Fujii T (2014) Second-order resonance among an array of two rows of vertical circular cylinders. Appl Ocean Res 47(2):192–198. CrossRefGoogle Scholar
  14. Kagemoto H, Yue DKP (1986) Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J Fluid Mech 166:189–209. CrossRefzbMATHGoogle Scholar
  15. Kamath A, Chella MA, Bihs H, Arntsen ØA (2015) CFD investigations of wave interaction with a pair of large tandem cylinders. Ocean Eng 108:738–748. CrossRefGoogle Scholar
  16. Linton CM, Evans DV (1990) The interaction of waves with arrays of vertical circular cylinders. J Fluid Mech 215:549–569. MathSciNetCrossRefzbMATHGoogle Scholar
  17. MacCamy RC, Fuchs RA (1954) Wave forces on piles: a diffraction theory. Tech. Memo No. 69, US Army Corps. of EngineersGoogle Scholar
  18. Maniar HD, Newman JN (1997) Wave diffraction by a long array of cylinders. J Fluid Mech 339:309–330. MathSciNetCrossRefzbMATHGoogle Scholar
  19. Mciver P (2002) Wave interaction with arrays of structures. Appl Ocean Res 24(3):121–126. CrossRefGoogle Scholar
  20. Ohkusu M (1969) On the heaving motion of two circular cylinders on the surface of a fluid. Reports of RIAM XVII(58):167–185Google Scholar
  21. Ohl COG, Taylor RE, Taylor PH, Borthwick AGL (2001) Water wave diffraction by a cylinder array. Part 1. Regular waves. J Fluid Mech 442:1–32. zbMATHGoogle Scholar
  22. Sankarbabu K, Sannasiraj SA, Sundar V (2007) Interaction of regular waves with a group of dual porous circular cylinders. Appl Ocean Res 29(4):180–190. CrossRefGoogle Scholar
  23. Siddorn P, Taylor RE (2008) Diffraction and independent radiation by an array of floating cylinders. Ocean Eng 35(13):1289–1303. CrossRefGoogle Scholar
  24. Ursell F (1951) Trapping modes in the theory of surface waves. Math Proc Camb Philos Soc 47(2):347–358. MathSciNetCrossRefzbMATHGoogle Scholar
  25. Walker DAG, Taylor RE, Taylor PH, Zang J (2008) Wave diffraction and near-trapping by a multi-column gravity-based structure. Ocean Eng 35(2):201–229. CrossRefGoogle Scholar
  26. Wang CZ, Wu GX (2007) Time domain analysis of second-order wave diffraction by an array of vertical cylinders. J Fluids Struct 23(4):605–631. CrossRefGoogle Scholar
  27. Zhan JM, Dong Z, Jiang W, Li YS (2010) Numerical simulation of wave transformation and runup incorporating porous media wave absorber and turbulence models. Ocean Eng 37(14):1261–1272. CrossRefGoogle Scholar
  28. Zhang ZG, He GH, Kashiwagi M, Wang ZK (2018) A quasi-cloaking phenomenon to reduce the wave drift force on an array of adjacent floating bodies. Appl Ocean Res 71:1–10. CrossRefGoogle Scholar

Copyright information

© Harbin Engineering University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Zhengke Wang
    • 1
  • Guanghua He
    • 1
    Email author
  • Zhigang Zhang
    • 1
  • Yanghan Meng
    • 1
  1. 1.School of Naval Architecture and Ocean EngineeringHarbin Institute of TechnologyWeihaiChina

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