Journal of Hydrodynamics

, Volume 30, Issue 4, pp 592–604 | Cite as

On the nonlinear transformation of breaking and non-breaking waves induced by a weakly submerged shelf

  • Giorgio ContentoEmail author
  • Guido Lupieri
  • Thomas Puzzer


The interaction of regular quasi-monochromatic waves with a weakly submerged rectangular shelf is studied by means of CFD simulations. The fundamental incident wave frequency is kept constant for the full set of simulated cases, while the incident wave amplitude is made increase progressively, so that the interaction with the shelf is dominated by almost inviscid non-linear flow for the smallest and by breaking for the highest incident waves. A parameter identification (PI) procedure is used to adapt a reduced model to the highly resolved time-space matrix of wave elevations obtained from the numerical simulations, on the weather and lee side respectively. In particular the wave number and the frequency of the component waves in the reduced model are left uncoupled, thus computed by the PI independently. The comparison of simulated data with experiments generally shows a very good agreement. Free/locked, incident/reflected, first/higher order wave components are quantified accurately by the PI and the energy transfer to super-harmonics is clearly evidenced. Moreover the results of the PI show clearly a very large increase in the phase speed of the higher order free waves on the lee side of the shelf, with increasing deviation from the linear behavior with increasing incident wave amplitude.

Key words

Nonlinear wave transformation submerged shelf wave breaking coupled space-time domain analysis reduced model parameter identification 


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The “Programma Attuativo Regionale del Fondo per lo Sviluppo e la Coesione (PAR FSC 2007-2013) Linea 3.1.2” is acknowledged for providing the support of the OpenViewSHIP Project.


  1. [1]
    Newman J. N. Propagation of water waves past long two-dimensional obstacles [J]. Journal of Fluid Mechanics, 1965, 23: 23–29.CrossRefzbMATHGoogle Scholar
  2. [2]
    Grue J. Nonlinear water waves at a submerged obstacle or bottom topography [J]. Journal of Fluid Mechanics, 1992, 244: 455–476.CrossRefGoogle Scholar
  3. [3]
    Ohyama T., Nadaoka K. Transformation of a nonlinear wave train passing over a submerged shelf without breaking [J]. Coastal Engineering, 1994, 24 (1–2): 1–22.CrossRefGoogle Scholar
  4. [4]
    Hsu T., Hsieh C., Hwang R. R. Using RANS to simulate vortex generation and dissipation around impermeable submerged double breakwaters [J]. Coastal Engineering, 2004, 51 (7): 557–579.CrossRefGoogle Scholar
  5. [5]
    Ting C. L., Lin M. C., Hsu C. M. Spatial variations of waves propagating over a submerged rectangular obstacle [J]. Ocean Engineering, 2005, 32 (11): 1448–1464.CrossRefGoogle Scholar
  6. [6]
    Sue Y. C., Cern M. J., Hwang R. R. Interaction of non-linear progressive viscous waves with a submerged obstacle [J]. Ocean Engineering, 2005, 32 (8–9): 893–923.CrossRefGoogle Scholar
  7. [7]
    Johnson H. K. Modelling of waves and currents around submerged breakwaters [J]. Coastal Engineering, 2005, 52 (10): 949–969.CrossRefGoogle Scholar
  8. [8]
    Johnson H. K., Karambas T. V., Avgeris I. et al. Wave modelling in the vicinity of submerged breakwaters [J]. Coastal Engineering, 2006, 53 (1): 39–48.CrossRefGoogle Scholar
  9. [9]
    Lu Y. J., Liu H., Wu W. et al. Numerical simulation of two-dimensional overtopping against seawalls armored with artificial units in regular waves [J]. Journal of Hydrodynamics, 2007, 19 (3): 322–329.CrossRefGoogle Scholar
  10. [10]
    Christou M., Swan C., Gudmestad O. T. The interaction of surface water waves with submerged breakwaters [J]. Coastal Engineering, 2008, 55 (12): 945–958.CrossRefGoogle Scholar
  11. [11]
    Guo X., Wang B., Liu H. et al. Numerical simulation of two-dimensional regular wave overtopping flows over the crest of a trapezoidal smooth impermeable sea dike [J]. Journal of Waterway Port Coastal and Ocean Engineering, 2014, 140 (3): 04014006.CrossRefGoogle Scholar
  12. [12]
    OpenFOAM. OpenFoam user guide [M]. Paris, France: OpenCFD Ltd, 2012.Google Scholar
  13. [13]
    Andersen T. L., Clavero M., Frigaard P. et al. A new active absorption system and its performance to linear and non-linear waves [J]. Coastal Engineering, 2016, 114: 47–60.CrossRefGoogle Scholar
  14. [14]
    Contento G., Codiglia R., D’Este F. Nonlinear effects in 2D transient nonbreaking waves in a closed flume [J]. Applied Ocean Research, 2001, 23 (1): 3–13.CrossRefGoogle Scholar
  15. [15]
    Higuera P., Lara L. J., Losada I. J. Realistic wave generation and active wave absorption for Navier-Stokes models application to OpenFOAM [J]. Coastal Engineering, 2013, 71: 102–118.CrossRefGoogle Scholar
  16. [16]
    Specialist Committee on CFD in Marine Hydrodynamics. Proceedings-Volume IIai][C]. 27th International Towing Tank Conference (ITTC), Copenhagen, Demark, 2014.Google Scholar
  17. [17]
    Swan C. Group discussion on wave quality in wave basins and accurate models for the design wave kinematics [C]. 27th International Towing Tank Conference (ITTC), Copenhagen, Demark, 2014.Google Scholar
  18. [18]
    Likke Andersen T., Clavero M., Frigaard P. et al. Decomposition of incident and reflected higher harmonic waves using four wave gauges [J]. Coastal Engineering, 2016, 51: 47–60.CrossRefGoogle Scholar
  19. [19]
    Rusche H. Computational fluid dynamics of dispersed two-phase flows at high phase fractions [M]. London. UK: Imperial College of Science, Technology and Medicine, 2002.Google Scholar
  20. [20]
    Contento G., Lupieri G., Jasak H. et al. Numerical study of unsteady breaking waves induced by a submerged hydro-foil at steady forward speed [C]. Proceedings of 18th International Conference on Ships and Shipping Research NAV’2015, Lecco, Italy, 2015, 104–114.Google Scholar
  21. [21]
    Lupieri G., Contento G. Numerical simulations of 2-D steady and unsteady breaking waves [J]. Ocean Engineering, 2015, 106: 298–316.CrossRefGoogle Scholar
  22. [22]
    Lupieri G., Contento G. On the wavy flow past a weakly submerged horizontal circular cylinder at low Keulegan Carpenter numbers [J]. Journal of Marine Science and Technology, 2017, 22 (9): 1–21.Google Scholar
  23. [23]
    Christensen E. D. Large eddy simulation of spilling and plunging breakers [J]. Coastal Engineering, 2006, 53 (5): 463–485.CrossRefGoogle Scholar
  24. [24]
    Shen L., Chan E. Application of a combined IB-VOF model to wavestructure interactions [J]. Applied Ocean Research, 2010, 32 (1): 40–48.CrossRefGoogle Scholar
  25. [25]
    Iafrati A., Campana E. F. Free-surface fluctuations behind microbreakers: Space-time behavior and subsurface flow field [J]. Journal of Fluid Mechanics, 2005, 529: 311–347.CrossRefzbMATHGoogle Scholar

Copyright information

© China Ship Scientific Research Center 2018

Authors and Affiliations

  • Giorgio Contento
    • 1
    Email author
  • Guido Lupieri
    • 1
  • Thomas Puzzer
    • 1
  1. 1.Department of Engineering and ArchitectureUniversity of TriesteTriesteItaly

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