Third-order theory for bichromatic bi-directional water waves

Journal of Fluid Mechanics

Volumn 557, Issue , 2006, Pages 369-397

  Medsen, Per A ^a   Fuhrman, David R ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; CURVE FITTING; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; VELOCITY;

BI-DIRECTIONAL WATER WAVES; BICHROMATIC WATER WAVES; FINITE DEPTH; FINITE-AMPLITUDE CARRIER WAVES; VELOCITY POTENTIAL;

WATER WAVES;

CONVERGENCE OF NUMERICAL METHODS; CURVE FITTING; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; VELOCITY; WATER WAVES;

FLUID MECHANICS; NONLINEAR WAVE; WATER WAVE; WAVE-WAVE INTERACTION;

EID: 33746067934     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112006009815     Document Type: Article

References (29)

1. Agnon, Y. 1993 On a uniformly valid model for surface wave interaction. J. Fluid Mech. 247, 589-601.
2. Bryant, P. J. 1985 Doubly periodic progressive permanent waves in deep water. J. Fluid Mech. 161, 27-42.
3. Chappelear, J. E. 1961 On the description of short-crested waves. Beach Erosion Board, US Army Corps Engrs. TM 125.
4. Cokelet, E. D. 1977 Steep gravity waves in water of arbitrary uniform depth. Phil. Trans. R. Soc. Lond. A 286, 183-230.
5. Fuchs, R. A. 1952 On the theory of short-crested oscillatory waves. Gravity Waves, US Natl Bur. Stand. Circular 521, 187-200.
6. Fuhrman, D. R., Madsen, P. A. & Bingham, H. B. 2004 A numerical study of crescent waves. J. Fluid Mech. 513, 309-341.
7. Hammack, J. L., Henderson, D. M. & Segur, H. 2005 Progressive waves with persistent two-dimensional surface patterns in deep water. J. Fluid Mech. 532, 1-51.
8. Hammack, J. L., Scheffner, N. & Segur, H. 1989 Two-dimensional periodic waves in shallow water. J. Fluid Mech. 209, 567-589.
9. Hogan, S. J., Gruman, I. & Stiassnie, M. 1988 On the changes in phase speed of one train of water waves in the presence of another. J. Fluid Mech. 192, 97-114.
10. Hsu, J. R. C., Tsuchiya, Y. & Silvester, R. 1979 Third-order approximation to short-crested waves. J. Fluid Mech. 90, 179-196.
11. Janssen, P. A. E. M. & Onorato, M. 2005 The shallow water limit of the Zakharov equation and consequences for (freak) wave prediction. TM 464. European Centre for Medium-Range Weather Forecasts (ECMWF), Reading, UK.
12. Kimmoun, O., Ioualalen, M. & Kharif, C. 1999 Instabilities of steep short-crested surface waves in deep water. Phys. of Fluids 11, 1679-1681.
13. Krasitskii, V. P. 1994 On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves. J. Fluid Mech. 272, 1-20.
14. Liu, Y. & Yue, D. K. P. 1998 On generalized Bragg scattering of surface waves by bottom ripples. J. Fluid Mech. 356, 297-326.
15. Longuet-Higgins, M. S. & Phillips, O. M. 1962 Phase velocity effects in tertiary wave interactions. J. Fluid Mech. 12, 333-336.
16. McLean, J. W. 1982 Instabilities of finite-amplitude gravity waves on water of finite depth. J. Fluid Mech. 114, 331-341.
17. Madsen, P. A., Fuhrman, D. R. & Wang, B. 2006 A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coastal Engng 53, 487-504.
18. Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. Part 1. The elementary interactions. J. Fluid Mech. 9, 193-217.
19. Pierson, W. J. JR. 1993 Oscillatory third-order perturbation solutions for sums of interacting long-crested Stokes waves on deep water. J. Ship Res. 37, 354-383.
20. Roberts, A. J. 1983 Highly nonlinear short-crested water waves. J. Fluid Mech. 135, 301-321.
21. Roberts, A. J. & Peregrine, D. H. 1983 Notes on long-crested water waves. J. Fluid Mech. 135, 323-335.
22. Roberts, A. J. & Schwartz, L. W. 1983 The calculation of nonlinear short-crested gravity waves. Phys. Fluids 26, 2388-2392.
23. Schäffer, H. A. 1996 Second-order wavemaker theory for irregular waves. Ocean Engng 23, 47-88.
24. Schäffer, H. A. & Steenberg, C. M. 2003 Second-order wavemaker theory for multidirectional waves. Ocean Engng 30, 1203-1231.
25. Sharma, J. & Dean, R. 1981 Second-order directional seas and associated wave forces. Soc. Pet. Engrs J. 129-140.
26. Stiassnie, M. & Shemer, L. 1984 On modifications of the Zakharov equation for surface gravity waves. J. Fluid Mech. 143, 47-67.
27. Zakharov, V. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. (Engl. Transl.) 9, 190-194.
28. Zakharov, V. 1999 Statistical theory of gravity and capilary waves on the surface of a finite depth fluid. Eur. J. Mech. B/Fluids 18, 327-344.
29. Zhang, J. & Chen, L. 1999 General third-order solutions for irregular waves in deep water. J. Engng Mech. 125, 768-779.