Boussinesq evolution equations: Numerical efficiency, breaking and amplitude dispersion

Coastal Engineering

Volumn 51, Issue 11-12, 2004, Pages 1117-1142

  Bredmose, H ^a,c   Schaffer H A ^b   Madsen, P A ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b DHI   (Denmark)

^c UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Amplitude dispersion; Boussinesq models; Computational efficiency; Deterministic modelling; Frequency domain modelling; Irregular waves; Roller model; Wave breaking

Indexed keywords

APPROXIMATION THEORY; FAST FOURIER TRANSFORMS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; WATER WAVES;

AMPLITUDE DISPERSIONS; BOUSSINESQ EVOLUTION EQUATIONS; NUMERICAL EFFICIENCY; TIME DOMAIN MODEL;

COASTAL ENGINEERING;

BOUSSINESQ EQUATION; MATHEMATICAL ANALYSIS; WAVE BEHAVIOR; WAVE BREAKING;

BOUSSINESQ EQUATION; MATHEMATICAL ANALYSIS; WAVE BREAKING; WAVE DISPERSION;

EID: 10244251673     PISSN: 03783839     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.coastaleng.2004.07.024     Document Type: Article

References (47)

1. M.B. Abbott J. Larsen P.A. Madsen J. Tao Simulation of wave breaking and runup Seminar on Hydrodynamics of Waves in Coastal Areas, 20th Congr. of IAHR 1983 IAHR Moscow
2. Y. Agnon A. Sheremet Stochastic nonlinear shoaling of directional spectra J. Fluid Mech. 345 1997 79-99
3. J.A. Battjes J.P.F.M. Janssen Energy loss and set-up due to breaking in random waves Proceedings of the 16th International Conference on Coastal Engineering 1978 ASCE 569-587
4. S. Beji J.A. Battjes Experimental investigation of wave propagation over a bar Coast. Eng. 19 1993 151-162
5. M. Brocchini M. Drago L. Iovenitti The modelling of short waves in shallow waters: Comparison of numerical models based on Boussinesq and Serre equations Proc. of the 23th Coast. Engng. Conf., Venice vol. 1 1992 ASCE Reston, VA 76-88
6. C. Canuto M.Y. Hussaini A. Quarteroni T.A. Zang Spectral Methods in Fluid Dynamics 1987 Springer New York
7. Y. Chen P.L.-F. Liu Modified Boussinesq equations and associated parabolic models for water wave propagation J. Fluid Mech. 288 1995 351-381
8. Y. Chen R.T. Guza S. Elgar Modeling spectra of breaking surface waves in shallow water J. Geophys. Res. 102 C11 1997 25035-25046
9. R. Deigaard Mathematical modelling of waves in the surf zone Progr. Rep. 69, ISVA, Technical University of Denmark, DK-2800 Lyngby, Denmark 1989 47-59
10. Y. Eldeberky J. Battjes Spectral modelling of wave breaking: Application to Boussinesq equations J. Geophys. Res. 101 C1 1996 1253-1264
11. S. Elgar R.T. Guza B. Raubenheimer T.H.C. Herbers E.L. Gallagher Spectral evolution of shoaling and breaking waves on a barred beach J. Geophys. Res. 102 C7 1997 15797-15805
12. Eliasen, E., Machenhauer, B., Rasmussen, E., 1970. On a numerical method for integration of the hydrodynamical equations with a spectral representation of the horizontal fields. Technical Report 2. Institut for Teoretisk Meterologi, University of Copenhagen
13. J.D. Fenton A fifth-order Stokes theory for steady waves J. Waterw. Port Coast. Ocean Eng. 111 2 1985 216-234
14. B. Fornberg G. Whitham A numerical and theoretical study of certain nonlinear wave phenomena Philos. Trans. R. Soc. Lond., A 289 1361 1978 373-404
15. M.H. Freilich R.T. Guza Nonlinear effects on shoaling surface gravity waves Philos. Trans. R. Soc. Lond., A 311 1984 1-41
16. 4 J. Fluid Mech. 405 2000 181-210
17. T.H.C. Herbers M.C. Burton Nonlinear shoaling of directionally spread waves on a beach J. Geophys. Res. 102 C9 1997 21101-21114
18. T.H.C. Herbers N.R. Russnogle S. Elgar Spectral energy balance of breaking waves within the surf zone J. Phys. Oceanogr. 30 11 2000 2723-2737
19. J.M. Kaihatu J.T. Kirby Nonlinear transformation of waves in finite water depth Phys. Fluids 7 8 1995 1903-1914
20. J.M. Kaihatu J.T. Kirby Two-dimensional parabolic modelling of extended Boussinesq equations J. Waterw. Port Coast. Ocean Eng. 127 1998 57-67
21. T. Karambas C. Koutitas A breaking wave propagation model based on the Boussinesq equations Coast. Eng. 18 1992 1-19
22. A.B. Kennedy Q. Chen J.T. Kirby R.A. Dalrymple Boussinesq modeling of wave transformation, breaking and runup: I. 1D J. Waterw. Port Coast. Ocean Eng. 126 2000 39-47
23. A.B. Kennedy J.T. Kirby Q. Chen R.A. Dalrymple Boussinesq-type equations with improved nonlinear behaviour Wave Motion 33 2001 225-243
24. P.L.-F. Liu S.B. Yoon J.T. Kirby Nonlinear refraction-diffraction of waves in shallow water J. Fluid Mech. 153 1985 185-201
25. P.A. Madsen H.A. Schäffer Higher-order Boussinesq-type equations for surface gravity waves: Derivation and analysis Philos. Trans. R. Soc. Lond., A 356 1998 3123-3184
26. P.A. Madsen O.R. Sørensen A new form of Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry Coast. Eng. 18 1992 183-204
27. P.A. Madsen O.R. Sørensen Bound waves and triad interactions in shallow water Ocean Eng. 20 1993 359-388
28. P.A. Madsen H.B. Bingham H. Liu A new Boussinesq method for fully nonlinear waves from shallow water to deep water J. Fluid Mech. 462 2002 1-30
29. P.A. Madsen O. Sørensen H.A. Schäffer Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and crossshore motion of regular waves Coast. Eng. 32 1997 255-287
30. P.A. Madsen O. Sørensen H.A. Schäffer Surf zone dynamics simulated by a Boussinesq type model. Part II: Surf beat and swash oscillations for wave groups and irregular waves Coast. Eng. 32 1997 289-320
31. H. Mase J.T. Kirby Hybrid frequency domain KdV equation for random wave transformation Proceedings of 23rd International Conference on Coastal Engineering, Venice 1992 ASCE Reston, VA 474-487
32. C.C. Mei Ü. Ünlüata Harmonic generation in shallow water waves. In: R.E. Meyer (Ed.). Waves on Beaches and Resulting Sediment Transport Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, The University of Wisconsin, and The Coastal Engineering Research Center U.S. Army, at Madison 1972 Academic Press New York
33. O. Nwogu An alternative form of the Boussinesq equations for nearshore wave propagation J. Waterw. Port Coast. Ocean Eng. 119 1993 618-638
34. S.A. Orszag Numerical methods for the simulation of turbulence Phys. Fluids 12 Suppl. III 1969 250-257
35. S.A. Orszag Transform method for calculation of vector coupled sums: application to the spectral form of the vorticity equation J. Atmos. Sci. 27 1970 890-895
36. D.H. Peregrine Long waves on a beach J. Fluid Mech. 27 1967 815-827
37. S. Sato M.B. Kabiling H. Suzuki Prediction of near-bottom velocity history by a nonlinear dispersive wave model Coast. Eng. Jpn. 35 1 1991 67-82
38. H.A. Schäffer P.A. Madsen R. Deigaard A Boussinesq model for waves breaking in shallow water Coast. Eng. 20 1993 185-202
39. R.E. Scraton Estimation of the truncation error in Runge-Kutta and allied processes Comput. J. 7 1964 246-248
40. O.R. Sørensen H.A. Schäffer L.S. Sørensen Boussinesq-type modelling using an unstructured finite element technique Coast. Eng. 50 2004 181-198
41. M.J.F. Stive Velocity and pressure field of spilling breakers Proc. of the 17th Coastal Engng. Conference 1980
42. I.A. Svendsen Wave heights and setup in a surf zone Coast. Eng. 8 1984 303-329
43. Tao, J., 1983. Computation of wave runup and wave breaking. Internal Report. Danish Hydraulic Institute, DK-2800 Hørsholm, Denmark. 40 pp.
44. F.C. Ting J.T. Kirby Observation of undertow and turbulence in a laboratory surf zone Coast. Eng. 24 1-2 1994 51-80
45. J. Veeramony I.A. Svendsen The flow in surf-zone waves Coast. Eng. 39 2000 93-122
46. G. Wei J.T. Kirby S.T. Grilli R. Subramanya A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves J. Fluid Mech. 294 1995 71-92
47. J.A. Zelt Runup of nonbreaking and breaking solitary waves Coast. Eng. 15 1991 205-246