Periodic wave patterns of two-dimensional Boussinesq systems

European Journal of Mechanics, B/Fluids

Volumn 25, Issue 4, 2006, Pages 393-405

  Chen, Min ^a   Iooss, Gérard ^b  

^a PURDUE UNIVERSITY   (United States)

^b INSTITUT UNIVERSITAIRE DE FRANCE   (France)

Author keywords

Bifurcation of travelling waves; Boussinesq systems; Periodic two dimensional pattern; Water waves

Indexed keywords

LYAPUNOV METHODS; MATHEMATICAL MODELS; NUMERICAL METHODS; SURFACE TENSION; WAVE EQUATIONS;

BOUSSINESQ SYSTEMS; PERIODIC TWO-DIMENSIONAL PATTERN; TRAVELING; TRAVELLING WAVE PATTERNS;

WATER WAVES;

EID: 33744923736     PISSN: 09977546     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechflu.2005.11.004     Document Type: Article

References (12)

1. Bona J.L., Colin T., and Lannes D. Long wave approximations for water waves. Arch. Rational Mech. Anal. 178 (2005) 373-410
2. Bona J.L., Chen M., and Saut J.-C. Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory. J. Nonlinear Sci. 12 (2002) 283-318
3. Hammack J., Scheffner N., and Segur H. Two-dimensional periodic waves in shallow water. J. Fluid Mech. 209 (1989) 567-589
4. Reeder J., and Shinbrot M. Three-dimensional, nonlinear wave interaction in water of constant depth. Nonlinear Anal. 5 (1981) 303-323
5. Craig W., and Nicholls D.P. Travelling two and three dimensional capillary gravity water waves. SIAM J. Math. Anal. 32 (2000) 323-359 (electronic)
6. Groves M.D., and Mielke A. A spatial dynamics approach to three-dimensional gravity-capillary steady water waves. Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 83-136
7. Groves M.D., and Haragus M. A bifurcation theory for three-dimensional oblique travelling gravity-capillary water waves. J. Nonlinear Sci. 13 (2003) 397-447
8. Bridges T.J., Dias F., and Menasce D. Steady three-dimensional water-wave patterns on a finite-depth fluid. J. Fluid Mech. 436 (2001) 145-175
9. Daripa P., and Dash R.K. A class of model equations for bi-directional propagation of capillary-gravity waves. Int. J. Engrg. Sci. 41 (2003) 201-218
10. Craig W., and Nicholls D.P. Traveling gravity water waves in two and three dimensions. Eur. J. Mech. B Fluids 21 (2002) 615-641
11. Hammack J., McCallister D., and Segur H. Two-dimensional periodic waves in shallow water. Part 2. Asymmetric waves. J. Fluid Mech. 285 (1995) 95-122
12. Hammack J., Henderson D., and Segur H. Progressive waves with persistent, two-dimensional surface patterns in deep water. J. Fluid Mech. 532 (2005) 1-52