Coupling between internal and surface waves

Natural Hazards

Volumn 57, Issue 3, 2011, Pages 617-642

  Craig, Walter ^a   Guyenne, Philippe ^b   Sulem, Catherine ^c  

^a MCMASTER UNIVERSITY   (Canada)

^b UNIVERSITY OF DELAWARE   (United States)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

Hamiltonian systems; Internal waves; Surface waves

Indexed keywords

AMPLITUDE; BOUSSINESQ EQUATION; COUPLING; FLUID DYNAMICS; INTERNAL WAVE; NONLINEAR WAVE; PERTURBATION; SURFACE WAVE; WAVE EQUATION; WAVE PROPAGATION;

EID: 79957883124     PISSN: 0921030X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11069-010-9535-4     Document Type: Article

References (26)

1. Benjamin TB (1966) Internal waves of finite amplitude and permanent form. J Fluid Mech 25: 241-270.
2. Benjamin TB (1967) Internal waves of permanent form of great depth. J Fluid Mech 29: 559-592.
3. Benjamin TB, Bridges TJ (1997) Reappraisal of the Kelvin-Helmholtz problem. I. Hamiltonian structure. J Fluid Mech 333: 301-325.
4. Bona JL, Lannes D, Saut J-C (2008) Asymptotic models for internal waves. J Math Pures Appl 89: 538-566.
5. Choi W, Camassa R (1999) Fully nonlinear internal waves in a two-fluid system. J Fluid Mech 396: 1-36.
6. Coifman R, Meyer Y (1985) Nonlinear harmonic analysis and analytic dependence. Pseudodifferential operators and applications (Notre Dame, 1984), 71-78. Proceedings of Symposia in Pure Mathematics, 43. American Mathematical Society, Providence, RI.
7. Colin T, Lannes D (2001) Long-wave short-wave resonance for nonlinear geometric optics. Duke Math J 107: 351-419.
8. Craig W, Groves M (1994) Hamiltonian long-wave approximations to the water-wave problem. Wave Motion 19: 367-389.
9. Craig W, Groves M (2000) Normal forms for waves in fluid interfaces. Wave Motion 31: 21-41.
10. Craig W, Guyenne P, Kalisch H (2004) A new model for large amplitude long internal waves. C R Mecanique 332: 525-530.
11. Craig W, Guyenne P, Kalisch H (2005a) Hamiltonian long-wave expansions for free surfaces and interfaces. Comm Pure Appl Math 58: 1587-1641.
12. Craig W, Guyenne P, Nicholls DP, Sulem C (2005b) Hamiltonian long-wave expansions for water waves over a rough bottom. Proc R Soc A 461: 839-873.
13. Craig W, Guyenne P, Sulem C (2010) A Hamiltonian approach to nonlinear modulation of surface water waves. Wave Motion. doi: 10. 1016/j. wavemoti. 2010. 04. 002.
14. Craig W, Nicholls DP (2002) Traveling gravity water waves in two and three dimensions. Eur J Mech B/Fluids 21: 615-641.
15. Craig W, Sulem C (1993) Numerical simulation of gravity waves. J Comput Phys 108: 73-83.
16. Dias F, Ilichev A (2001) Interfacial waves with free-surface boundary conditions: an approach via a model equation. Physica D 150: 278-300.
17. Duchêne V (2009) Asymptotic shallow water models for internal waves in a two-fluid system with a free surface. Preprint, ArXiv: 0906. 0839v1.
18. Fazioli C, Nicholls DP (2008) Parametric analyticity of functional variations of Dirichlet-Neumann operators. Diff Int Eq 21: 541-574.
19. Gear J, Grimshaw R (1984) Weak and strong interactions between internal solitary waves. Stud Appl Math 70: 235-258.
20. Global Ocean Associates (2002) Contribution to An atlas of internal solitary waves: The Andaman Sea. Report prepared for the Office of Naval Research, code 322PO.
21. Hashizume Y (1980) Interaction between short surface waves and long internal waves. J Phys Soc Japan 48: 631-638.
22. Landau LD, Lifshitz EM (1960) Mechanics. Pergamon Press, Oxford-London-New York-Paris.
23. Osborne AR, Burch TL (1980) Internal solitons in the Andaman Sea. Science 208: 451.
24. Parau E, Dias F (2001) Interfacial periodic waves of permanent form with free-surface boundary conditions. J Fluid Mech 437: 325-336.
25. Peters AD, Stoker JJ (1960) Solitary waves in liquids having non-constant density. Comm Pure Appl Math 13: 115-164.
26. Zakharov VE (1968) Stability of periodic waves of finite amplitude on the surface of a deep fluid. J Appl Mech Tech Phys 9: 190-194.