A model for strongly nonlinear long interfacial waves with background shear

Studies in Applied Mathematics

Volumn 133, Issue 2, 2014, Pages 182-213

  Boonkasame, Anakewit ^a   Milewski, Paul A ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b UNIVERSITY OF BATH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COASTAL ENGINEERING; KORTEWEG-DE VRIES EQUATION; NONLINEAR EQUATIONS; SHEAR FLOW; WATER WAVES;

BOTTOM WALL; DIFFERENT DENSITIES; INTERFACIAL WAVES; INVISCID FLUIDS; NON-HYDROSTATIC; NONLINEAR WAVES; REGULARISATION; STRONGLY NONLINEAR; SYSTEMS OF EQUATIONS; TWO-LAYER;

SOLITONS;

EID: 84905382427     PISSN: 00222526     EISSN: 14679590     Source Type: Journal    
DOI: 10.1111/sapm.12036     Document Type: Article

References (22)

1. D. R. Christie, The morning glory of the Gulf of Carpentaria, Aust. Meteorol. Mag. 41:21-60 (1992).
2. R. B. Perry and G. R. Schimke, Large amplitude internal waves observed off the north-west coast of Sumatra, J. Geophys. Res. 70:2319-2324 (1965).
3. D. J. Benney, Long nonlinear waves in fluid flows, J. Math. Phys. 45:52-63 (1966).
4. R. Long, Long waves in a two-fluid system, J. Meteorol. 13:70-74 (1956).
5. L. V. Ovsyannikov, Two-layer shallow-water model, J. Appl. Mech. Tech. Phys. 20:127-135 (1979).
6. R. Liska, L. Margolin, and B. Wendroff, Nonhydrostatic two-layer models of incompressible flow, Comp. Math. Appl. 29:25-37 (1995).
7. W. Choi and R. Camassa, Fully nonlinear internal waves in a two-fluid system, J. Fluid Mech. 396:1-36 (1999).
8. M. Funakoshi and M. Oikawa, Long internal waves of large amplitude in a two-layer fluid, J. Phys. Soc. Jpn. 55:128-144 (1986).
9. M. Miyata, An internal solitary wave of large amplitude., La Mer. 23:43-48 (1985).
10. H. Michallet and E. Barthélemy, Experimental study of interfacial solitary waves, J. Fluid Mech. 366:159-177 (1998).
11. T. P. Stanton and L. Ostrovsky, Observations of highly nonlinear internal solitons over the continental shelf, Geophys. Res. Lett. 25:2695-2698 (1998).
12. R. Camassa, W. Choi, H. Michallet, P.-O. Rusås, and J. K. Sveen, On the realm of validity of strongly nonlinear asymptotic approximations for internal waves, J. Fluid Mech. 549:1-23 (2006).
13. T.-C. Jo and W. Choi, Dynamics of strongly nonlinear internal solitary waves in shallow water, Stud. Appl. Math. 109:205-227 (2002).
14. J. Grue, A. Jensen, P.-O. Rusas, and J. K. Sveen, Properties of large-amplitude internal waves, J. Fluid Mech. 380:257-278 (1999).
15. A. Boonkasame and P. A. Milewski, The stability of large-amplitude shallow interfacial non-Boussinesq flows, Stud. Appl. Math. 128:40-58 (2011).
16. J. L. Bona, M. Chen, and J.-C. Saut, Boussinesq equations and other systems for small amplitude long waves in nonlinear dispersive media. I: derivation and linear theory, J. Nonlinear Sci. 12:283-318 (2002).
17. H. Y. Nguyen and F. Dias, A Boussinesq system for two-way propagation of interfacial waves, Physical D 237:2365-2389 (2008).
18. R. Camassa, P.-O. Rusås, A. Saxena, and R. Tiron, Fully nonlinear periodic internal waves in a two-fluid system of finite depth, J. Fluid Mech. 652:259-298 (2010).
19. W. Choi, R. Barros, and T.-C. Jo, A regularized model for strongly nonlinear internal solitary waves, J. Fluid Mech. 629:73-85 (2009).
20. L. Chumakova, F. E. Menzaque, P. A. Milewski, R. R. Rosales, E. G. Tabak, and C. V. Turner, Stability properties and nonlinear mappings of two and three-layer stratified flows, Stud. Appl. Math. 122:123-137 (2009).
21. F. Dias and J.-M. Vanden-Broeck, On internal fronts, J. Fluid Mech. 479:145-154 (2003).
22. R. Grimshaw, E. Pelinovsky, and T. Talipova, The modified Korteweg-de Vries equation in the theory of large-amplitude internal waves, Nonlinear Proc. Geophys. 4:237-250 (1997).