Breaking solitary waves and breaking wave forces on a vertically mounted slender cylinder over an impermeable sloping seabed

  • Mayilvahanan Alagan ChellaEmail author
  • Hans Bihs
  • Dag Myrhaug
  • Michael Muskulus
Research Article


In the present study, breaking solitary waves over a sloping seabed and breaking wave forces on a vertically mounted cylinder are simulated with the three-dimensional CFD model REEF3D. The numerical model uses the Reynolds-Averaged Navier–Stokes (RANS) equations together with the level set method (LSM) for the free surface and the \(k-\omega \) for the turbulence. The numerical model is validated for simulating breaking solitary waves and breaking wave forces against the experimentally measured free surface profiles and vertical and horizontal velocities by Mo et al. (Ocean Eng 74:48–60, 2013) and the experimentally measured free surface elevation and breaking wave force by Chakrabarti et al. (Appl Ocean Res 19:113–140, 1997). The main purpose of the paper is to examine the effects of the breaking characteristics, the geometric properties, the relative cylinder positions and the incident wave heights on the breaking wave force characteristics. A total of 21 simulations are performed to investigate the characteristics and the geometric properties of solitary waves breaking over a slope and the associated breaking wave forces on a cylinder. First, the characteristics and geometric properties of breaking solitary waves are investigated with two-dimensional simulations. Further, the study explores the effect of the relative distance between the breaking point and the cylinder on breaking wave forces. Finally, the study examines breaking solitary wave forces for different incident waves. This also includes the analysis of breaking wave force characteristics such as the impact duration and rise time, the peak force, the average slamming coefficient and the force impulse. The results of the numerical simulations show that the relative distance between the cylinder and the breaking point plays an important role in obtaining the maximum force. In addition, the numerical model is capable of representing the most important physical flow features related to the breaking solitary waves and the interaction with the vertical slender cylinder.


Solitary waves Wave structure interaction Breaking waves Geometric properties Breaking characteristics Breaking wave forces 



The authors wish to thank Prof. Atle Jansen and Prof. Phillip L.-F. Liu for providing the experimental data. The research for this paper was supported by the Norwegian Research Center for Offshore Wind Technology (NOWITECH), Research council of Norway (Contract No.193823). The authors also wish to thank NOTUR (Project No. NN9240K) for the allocation of computational resources provided on the Vilje system at the super computing facilities at NTNU.


  1. Adeyemo M (1968) Effect of beach slope and shoaling on wave asymmetry. In: Proceedings of the 11-th Conference on Coastal Engineering, pp 145–172Google Scholar
  2. Alagan Chella M, Bihs H, Myrhaug D, Muskulus M (2015a) Breaking characteristics and geometric properties of spilling breakers over slopes. Coast Eng 95:4–19CrossRefGoogle Scholar
  3. Alagan Chella M, Bihs H, Myrhaug D (2015b) Characteristics and profile asymmetry properties of waves breaking over an impermeable submerged reef. Coast Eng 100:26–36CrossRefGoogle Scholar
  4. Alagan Chella M, Bihs H, Myrhaug D, Muskulus M (2015) Hydrodynamic characteristics and geometric properties of plunging and spilling breakers over impermeable slopes. Ocean Model. doi: 10.1016/j.ocemod.2015.11.011
  5. Alagan Chella M, Tørum A, Myrhaug D (2012) An overview of wave impact forces on offshore wind turbine substructures. Energy Procedia 20:217–226CrossRefGoogle Scholar
  6. Arntsen ØA, Ros X, Tørum A (2011) Impact forces on a vertical pile from plunging breaking waves. In: Proceedings of the 24th Conference on Coastal structuresGoogle Scholar
  7. Bihs H, Kamath A, Alagan Chella M, Arntsen ØA (2016) Breaking wave interaction with tandem cylinders under different impact scenarios. J Port Coast Ocean Eng Waterw. doi: 10.1061/(ASCE)WW.1943-5460.0000343
  8. Camfield F, Street R (1979) Shoaling of solitary waves on small slopes. J Waterw Port Coast Ocean Div 95:1–22Google Scholar
  9. Chakrabarti SK, Kriebel D, Berek E (1997) Forces on a single pile caisson in breaking waves and current. Appl Ocean Res 19:113–140CrossRefGoogle Scholar
  10. Chaplin J, Flintham T, Greated C, Skyner D (1992) Breaking wave forces on a vertical cylinder. Technical report, Health and Safety Executive, London, UKGoogle Scholar
  11. Choi S, Lee K, Gudmestad O (2015) The effect of dynamic amplification due to a structures vibration on breaking wave impact. Ocean Eng 96:8–20CrossRefGoogle Scholar
  12. Chorin A (1968) Numerical solution of the Navier–Stokes equations. Math Comput 22:745–762MathSciNetCrossRefzbMATHGoogle Scholar
  13. Cooker MJ, Peregrine DH (1990) A model for breaking wave impact pressures. In: Proceedings of the 22nd Conference on Coastal Engineering, pp 1473–1486Google Scholar
  14. Cooker MJ, Peregrine DH (1995) Pressure-impulse theory for liquid impact problems. J Fluid Mech 297:193–214MathSciNetCrossRefzbMATHGoogle Scholar
  15. Cuomo G, Piscopia R, Allsop W (2011) Evaluation of wave impact loads on caisson breakwaters based on joint probability of impact maxima and rise times. Coast Eng 58:9–27CrossRefGoogle Scholar
  16. Cuomo G, Tirindelli M, Allsop W (2007) Breaking wave loads at vertical seawalls and breakwaters. Coast Eng 54:657–679CrossRefGoogle Scholar
  17. Cuomo G, Allsop W, Bruce T, Pearson J (2010) Breaking wave loads at vertical seawalls and breakwaters. Coast Eng 57:424–439CrossRefGoogle Scholar
  18. Fenton J (1985) A fifth-order stokes theory for steady waves. J Waterw Port Coast Ocean Eng 111(2):216–234CrossRefGoogle Scholar
  19. Galvin CJ (1968) Breaker type classification on three laboratory beaches. J Geophys Res 73(12):3651–3659CrossRefGoogle Scholar
  20. Goda Y, Haranaka S, Kitahata M (1966) Study of impulsive breaking wave forces on piles. Technical report, Port and Harbor Research Institute, Ministry of TransportGoogle Scholar
  21. Goring DG (1978) Tsunamis-the propagation of long waves onto a shelf, PhD thesis, California Institute of TechnologyGoogle Scholar
  22. Grilli ST, Subramanya R, Svendsen IA, Veeramony J (1995) Shoaling of solitary waves on plane beaches. J Waterw Port Coast Ocean Eng 120(6):609–628CrossRefGoogle Scholar
  23. Grilli ST, Svendsen IA, Subramanya R (1997) Breaking criterion and characteristics for solitary waves on slopes. J Waterw Port Coast Ocean Eng 123(3):102–112CrossRefGoogle Scholar
  24. Grimshaw R (1971) The solitary wave in water of variable depth. Part 2. J Fluid Mech 46:611–622CrossRefzbMATHGoogle Scholar
  25. Hattori M, Arami A, Yui T (1994) Wave impact pressure on vertical walls under breaking waves of various types. Coast Eng 22:79–114CrossRefGoogle Scholar
  26. Hieu PD, Katsutoshi T, Ca VT (2004) Numerical simulation of breaking waves using a two-phase flow model. Appl Math Model 28(11):983–1005CrossRefzbMATHGoogle Scholar
  27. Hwang PA (1984) Profile asymmetry of shoaling waves on a mild slope. In: Proceedings of the 19th Conference on Coastal Engineering, pp 1016–1027Google Scholar
  28. Ippen AT, Kulin G (1954) The shoaling and breaking of the solitary wave. In: Proceedings of the 5th Conference on Coastal Engineering, pp 27–47Google Scholar
  29. Irschik K, Sparboom U, Oumeraci H (2002) Breaking wave characteristics for the loading of a slender pile. In: Proceedings of the 28th Conference on Coastal Engineering, pp 1341–1352Google Scholar
  30. Jacobsen NG, Fuhrman DR, Fredsøe J (2012) A wave generation toolbox for the open-source CFD library : OpenFoam. Int J Numer Methods Fluids 70(November):1073–1088MathSciNetCrossRefGoogle Scholar
  31. Jiang GS, Shu CW (1996) Efficient implementation of weighted ENO schemes. J Comput Phys 126:202–228MathSciNetCrossRefzbMATHGoogle Scholar
  32. Kamath A, Alagan Chella M, Bihs H, Arntsen ØA (2015) CFD investigations of wave interaction with a pair of large tandem cylinders. Ocean Eng 108:734–748CrossRefGoogle Scholar
  33. Kamath A, Bihs H, Alagan Chella M, Arntsen ØA (2016) Upstream-cylinder and downstream-cylinder influence on the hydrodynamics of a four-cylinder group. J Port Coast Ocean Eng Waterw. doi: 10.1061/(ASCE)WW.1943-5460.0000339
  34. Kjeldsen SP, Myrhaug D (1978) Kinematics and dynamics of breaking waves. Technical report, River and Harbour Laboratory (NHL), The Norwegian Institute of TechnologyGoogle Scholar
  35. Kortenhaus A, Oumeraci H, Allsop N, McConnell K, Van Gelder P, Hewson P, Walkden M, Müller G, Calabrese M, Vicinanza D (1999) Wave impact loads-pressures and forces. In: Final Proceedings, MAST III, PROVERBS-Project: Vol. Hydrodynamic Aspects, IIaGoogle Scholar
  36. Larsen J, Dancy H (1983) Open boundaries in short wave simulations—a new approach. Coast Eng 7:285–297CrossRefGoogle Scholar
  37. Lemos CM (1992) A simple numerical technique for turbulent flows with free surfaces. Int J Numer Methods Fluids 15:127–146CrossRefzbMATHGoogle Scholar
  38. Lin P, Liu PL-F (1998) A numerical study of breaking waves in the surf zone. J Fluid Mech 359:239–264CrossRefzbMATHGoogle Scholar
  39. Losada MA, Vidal C, Medina R (1989) Experimental study of the evolution of a solitary wave at an abrupt junction. J Geophys Res 94:14557–14566CrossRefGoogle Scholar
  40. Miles JW (1980) Solitary waves. Annu Rev Fluid Mech 12:11–43CrossRefzbMATHGoogle Scholar
  41. Mo W, Jensen A, Liu PL-F (2013) Plunging solitary wave and its interaction with a slender cylinder on a sloping beach. Ocean Eng 74:48–60CrossRefGoogle Scholar
  42. Munk WH (1949) The solitary wave theory and its application to surf problems. Ann N Y Acad Sci 3:376–424MathSciNetCrossRefGoogle Scholar
  43. Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent Speed: Algorithms based on Hamilton–Jacobi formulations. J Comput Phys 79:12–49MathSciNetCrossRefzbMATHGoogle Scholar
  44. Peregrine DH (2003) Water-wave impact on walls. Annu Rev Fluid Mech 35:23–43MathSciNetCrossRefzbMATHGoogle Scholar
  45. Sarpkaya T, Isaacson M (1981) Mechanics of Wave Forces on Offshore Structures, Van Nostrand Reinhold CompanyGoogle Scholar
  46. Sawaragi T, Nochino M (1984) Impact forces of nearly breaking waves on a vertical circular cylinder. Coast Eng J 27:249–263Google Scholar
  47. Shu CW, Osher S (1988) Efficient implementation of essentially non-oscillatory shock capturing schemes. J Comput Phys 77:439–471MathSciNetCrossRefzbMATHGoogle Scholar
  48. Stive M, Wind H (1982) A study of radiation stress and set-up in the nearshore region. Coast Eng 6:1–26CrossRefGoogle Scholar
  49. Ting FCK, Kirby JT (1994) Observation of undertow and turbulence in a laboratory surf zone. Coast Eng 24(1–2):51–80CrossRefGoogle Scholar
  50. van der Vorst H (1992) Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J Sci Stat Comput 13:631–644MathSciNetCrossRefzbMATHGoogle Scholar
  51. Wienke J, Oumeraci H (2005) Breaking wave impact force on a vertical and inclined slender pile-theoretical and large-scale model investigations. Coast Eng 52:416–435CrossRefGoogle Scholar
  52. Wienke J, Sparboom U, Oumeraci H (2000) Breaking wave impact on a slender cylinder. In: Proceedings of the 27th Conference on Coastal Engineering, pp 1787–1798Google Scholar
  53. Xiao H, Huang W (2014) Three-dimensional numerical modeling of solitary wave breaking and force on a cylinder pile in a coastal surf zone. J Eng Mech ASCE 141(8):A4014001Google Scholar
  54. Xie Z (2013) Two-phase flow modelling of spilling and plunging breaking waves. Appl Math Model 37:3698–3713MathSciNetCrossRefGoogle Scholar
  55. Zhao Q, Armfield S, Tanimoto K (2004) Numerical simulation of breaking waves by a multi-scale turbulence model. Coast Eng 51(1):53–80CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Civil and Transport EngineeringNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Department of Marine TechnologyNorwegian University of Science and TechnologyTrondheimNorway

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