A new approach to handle wave breaking in fully non-linear Boussinesq models

Coastal Engineering

Volumn 67, Issue , 2012, Pages 54-66

  Tissier, M ^a   Bonneton, P ^a   Marche, F ^b   Chazel, F ^c   Lannes, D ^d  

^a UNIVERSITÉ DE BORDEAUX   (France)

^b UNIVERSITÉ DE MONTPELLIER   (France)

^c CNRS   (France)

^d ÉCOLE NORMALE SUPÉRIEURE   (France)

Author keywords

Breaking model; Finite volume; Fully non linear Boussinesq model; Shock theory

Indexed keywords

BOUSSINESQ MODEL; BOUSSINESQ-TYPE MODELS; BREAKING MODEL; BREAKING WAVES; FINITE VOLUME; GOVERNING EQUATIONS; GREEN-NAGHDI; NON-LINEAR SHALLOW WATER EQUATIONS; SHOCK THEORY; TIME STEP; WAVEBREAKING;

DISPERSION (WAVES); ENERGY DISSIPATION; EQUATIONS OF MOTION; OCEANOGRAPHY; WAVEFRONTS;

WATER WAVES;

BOUSSINESQ EQUATION; FINITE VOLUME METHOD; NUMERICAL MODEL; SHALLOW-WATER EQUATION; WAVE BREAKING;

EID: 84860791117     PISSN: 03783839     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.coastaleng.2012.04.004     Document Type: Article

References (66)

1. Alvarez-Samaniego B., Lannes D. Large time existence for 3D water-waves and asymptotics. Invent. Math. 2008, 171:485-541.
2. Audusse E., Bouchut F., Bristeau M., Klein R., Perthame B. A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM Journal on Scientific Computing 2004, 25:2050-2065.
3. Beji S., Battjes J.A. Experimental investigation of wave propagation over a bar. Coastal Engineering 1993, 19:151-162.
4. Berthon C., Marche F. A positive preserving high order VFRoe scheme for shallow water equations: a class of relaxation schemes. SIAM Journal on Scientific Computing 2008, 30:2587-2612.
5. Berthon C., Marche F., Turpault R. An efficient scheme on wet/dry transitions for shallow water equations with friction. Computer and Fluids 2011, 48.
6. Bjørkavåg M., Kalisch H. Wave breaking in Boussinesq models for undular bores. Physics Letters A 2011, 375:1570-1578.
7. Bonneton P. Modelling of periodic wave transformation in the inner surf zone. Ocean Engineering 2007, 34:1459-1471.
8. Bonneton P., Bruneau N., Marche F., Castelle B. Large-scale vorticity generation due to dissipating waves in the surf zone. Discrete and Continuous Dynamical Systems-Series B 2010, 13:729-738.
9. Bonneton P., Barthelemy E., Chazel F., Cienfuegos R., Lannes D., Marche F., Tissier M. Recent advances in Serre-Green Naghdi modelling for wave transformation, breaking and runup processes. European Journal of Mechanics-B/Fluids 2011, 30:589-597.
10. Bonneton P., Chazel F., Lannes D., Marche F., Tissier M. A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model. Journal of Computational Physics 2011, 230:1479-1498.
11. Briganti R., Brocchini M., Bernetti R. An operator-splitting approach for Boussinesq-type equations. GIMC 2004, XV Congresso Italiano di Meccanica Computazionale-AIMETA 2004.
12. Brocchini M., Dodd N. Nonlinear shallow water equation modeling for coastal engineering. Journal of Waterway, Port, Coastal, and Ocean Engineering 2008, 134:104-120.
13. Bruno D., Serio F.D., Mossa M. The FUNWAVE model application and its validation using laboratory data. Coastal Engineering 2009, 56:773-787.
14. Bühler O. On the vorticity transport due to dissipating or breaking waves in shallow-water flow. Journal of Fluid Mechanics 2000, 407:235-263.
15. Carter J.D., Cienfuegos R. The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations. European Journal of Mechanics - B/Fluids 2011, 30:259-268.
16. Chanson H. Turbulence in positive surges and tidal bores. effects of bed roughness and adverse bed slopes 2008, Hydraulic Model Report No. CH68/08, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, 121 pages.
17. Chazel F., Lannes D., Marche F. Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model. Journal of Scientific Computing 2010, 1-12.
18. Cienfuegos R., Barthélemy E., Bonneton P. A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part I: model development and analysis. International Journal for Numerical Methods in Fluids 2006, 51:1217-1253.
19. Cienfuegos R., Barthélemy E., Bonneton P. Wave-breaking model for Boussinesq-type equations including roller effects in the mass conservation equation. Journal of Waterway, Port, Coastal, and Ocean Engineering 2010, 136:10-26.
20. Cox, D.T., 1995. Experimental and numerical modelling of surf zone hydrodynamics. Ph.D. thesis. University of Delaware, Newark, Del.
21. Duncan J.H. An experimental investigation of breaking waves produced by a towed hydrofoil. Proceedings of the Royal Society of London. Series A 1981, 377:331-348.
22. Elgar S., Gallagher E.L., Guza R.T. Nearshore sandbar migration. Journal of Geophysical Research 2001, 106(C6):11623-11627.
23. Erduran K.S. Further application of hybrid solution to another form of Boussinesq equations and comparisons. International Journal for Numerical Methods in Fluids 2007, 53:827-849.
24. Erduran K.S., Ilic S., Kutija V. Hybrid finite-volume finite-difference scheme for the solution of Boussinesq equations. International Journal for Numerical Methods in Fluids 2005, 49:1213-1232.
25. Favre H. Etude théorique et expérimentale des ondes de translation dans les canaux découverts 1935, Dunod, Paris.
26. Grasso F., Michallet H., Barthélemy E. Sediment transport associated with morphological beach changes forced by irregular asymmetric, skewed waves. Journal of Geophysical Research 2011, 116.
27. Green A.E., Naghdi P.M. A derivation of equations for wave propagation in water of variable depth. Journal of Fluid Mechanics 1976, 78:237-246.
28. Grue J., Pelinovsky E.N., Fructus D., Talipova T., Kharif C. Formation of undular bores and solitary waves in the Strait of Malacca caused by the 26 December 2004 Indian Ocean tsunami. Journal of Geophysical Research C: Oceans 2008, 113.
29. Haller M.C., Catalán P.A. Remote sensing of wave roller lengths in the laboratory. Journal of Geophysical Research 2010, 114.
30. Hsiao S.C., Lin T.C. Tsunami-like solitary waves impinging and overtopping an impermeable seawall: experiment and RANS modeling. Coastal Engineering 2010, 57:1-18.
31. Kennedy A.B., Chen Q., Kirby J.T., Dalrymple R.A. Boussinesq modeling of wave transformation, breaking and run-up. I: one dimension. ASCE Journal of Waterway, Port, Coastal and Ocean Engineering 2000, 126(1):48-56.
32. Kirby J.T., Wei G., Chen Q., Kennedy A.B., Dalrymple R.A. FUNWAVE 1.0. Fully nonlinear Boussinesq wave model. Documentation and user's manual. Technical Report CACR-98-06 1998, Center for Applied Coastal Research, Department of Civil and Environmental Engineering, University of Delaware.
33. Kobayashi N., Silva G.D., Watson K. Wave transformation and swash oscillation on gentle and steep slopes. Journal of Geophysical Research 1989, 94:951-966.
34. Lannes D., Bonneton P. Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation. Physics of Fluids 2009, 21.
35. Lin P., Liu P.L.F. A numerical study of breaking waves in the surf zone. Journal of Fluid Mechanics 1998, 359:239-264.
36. Lynett P.J. Nearshore wave modeling with high-order Boussinesq-type equations. Journal of Waterway, Port, Coastal and Ocean Engineering 2006, 132.
37. Madsen P.A., Sørensen O.R., Schäffer H.A. Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves. Coastal Engineering 1997, 32:255-287.
38. Marche F., Bonneton P., Fabrie P., Seguin N. Evaluation of well-balanced bore-capturing schemes for 2D wetting and drying processes. International Journal for Numerical Methods in Fluids 2007, 53:867-894.
39. Miles J., Salmon R. Weakly dispersive nonlinear gravity waves. Journal of Fluid Mechanics 1985, 157:519-531.
40. Nwogu O. Alternative form of Boussinesq equations for nearshore wave propagation. Journal of Waterway, Port, Coastal and Ocean Engineering 1993, 119:618-638.
41. Okamoto T., Basco D. The relative trough Froude number for initiation of wave breaking: theory, experiments and numerical model confirmation. Coastal Engineering 2006, 53:675-690.
42. Orszaghova J., Borthwick A.G., Taylor P.H. From the paddle to the beach-a Boussinesq shallow water numerical wave tank based on Madsen and Sørensen's equations. Journal of Computational Physics 2012, 231:328-344.
43. Peregrine D.H. Breaking waves on beaches. Annual Review of Fluid Mechanics 1983, 15:149-178.
44. Peregrine D. Surf zone currents. Theoretical and Computational Fluid Dynamics 1998, 10:295-309.
45. Roelvink D., Reniers A., van Dongeren A., van Thiel de Vries J., McCall R., Lescinski J. Modelling storm impacts on beaches, dunes and barrier islands. Coastal Engineering 2009, 56:1133-1152.
46. Ruessink B.G., Van Den Berg T.J.J., Van Rijn L.C. Modeling sediment transport beneath skewed asymmetric waves above a plane bed. Journal of Geophysical Research C: Oceans 2009, 114.
47. Schäffer H.A., Madsen P.A., Deigaard R. A Boussinesq model for waves breaking in shallow water. Coastal Engineering 1993, 20:185-202.
48. Serre F. Contribution à l'étude des écoulements permanents et variables dans les canaux. Houille Blanche 1953, 8:374-388.
49. Shi F., Kirby J.T., Harris J.C., Geiman J.D., Grilli S.T. A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation. Ocean Modelling 2012, 43-44:36-51.
50. Shiach J.B., Mingham C.G. A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations. Coastal Engineering 2009, 56:32-45.
51. Smith J.A. Wave-current interactions in finite depth. Journal of Physical Oceanography 2006, 36.
52. Soares-Frazão S., Guinot V. A second-order semi-implicit hybrid scheme for one-dimensional Boussinesq-type waves in rectangular channels. International Journal for Numerical Methods in Fluids 2008, 58:237-261.
53. Soares-Frazão S., Zech Y. Undular bores and secondary waves-experiments and hybrid finite-volume modeling. Journal of Hydraulic Research, International Association of Hydraulic Engineering and Research (IAHR) 2002, 40:33-43.
54. Stocker J.J. Water Waves-The Mathematical Theory With Applications 1957, Interscience Publishers, Inc.
55. Synolakis C.E. The runup of solitary waves. Journal of Fluid Mechanics 1987, 185:523-545.
56. Ting F.C., Kirby J.T. Observation of undertow and turbulence in a laboratory surf zone. Coastal Engineering 1994, 24:51-80.
57. Tissier M., Bonneton P., Marche F., Chazel F., Lannes D. Nearshore dynamics of tsunami-like undular bores using a fully nonlinear Boussinesq model. Journal of Coastal Research SI 2011, 64.
58. Tonelli M., Petti M. Hybrid finite volume-finite difference scheme for 2DH improved Boussinesq equations. Coastal Engineering 2009, 56:609-620.
59. Tonelli M., Petti M. Finite volume scheme for the solution of 2D extended Boussinesq equations in the surf zone. Ocean Engineering 2010, 37:567-582.
60. Tonelli M., Petti M. Shock-capturing Boussinesq model for irregular wave propagation. Coastal Engineering 2012, 61:8-19.
61. Treske A. Undular bores (Favre-waves) in open channels-experimental studies. Journal of Hydraulic Research 1994, 32:355-370.
62. Wei G., Kirby J.T., Grilli S.T., Subramanya R. A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves. Journal of Fluid Mechanics 1995, 294:71-92.
63. Weston B.P., Taylor P.H., Borthwick A.G.L., Hunt A.C. Godunov-type Boussinesq modelling of extreme wave run-up. Shallow Flows: Research Presented at the International Symposium on Shallow Flows, Delft, Netherlands 2003, 98-403.
64. Yasuda H. One-dimensional study on propagation of tsunami wave in river channels. Journal of Hydraulic Engineering ASCE 2010, 136.
65. Zelt J.A. The run-up of nonbreaking and breaking solitary waves. Coastal Engineering 1991, 15:205-246.
66. Zijlema M., Stelling G.S., Smit P. SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters. Coastal Engineering 2011, 58:992-1012.