Numerical study of interfacial solitary waves propagating under an elastic sheet

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 470, Issue 2168, 2014, Pages

  Wang, Zhan ^a   Pãrãu, Emilian I ^b   Milewski, Paul A ^c   Vanden Broeck, Jean Marc ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF EAST ANGLIA   (United Kingdom)

^c University of Bath   (United Kingdom)

Author keywords

Generalized solitary wave; Interfacial wave; Ravity flexural; Solitary wave

Indexed keywords

ELASTICITY; FLUIDS;

BOUNDARY INTEGRAL METHODS; CONSTANT DENSITY; FULLY NONLINEAR; INTERFACIAL WAVES; INTERNAL MODES; INTERNAL WAVES; PERIODIC TRAINS; RAVITY-FLEXURAL;

SOLITONS;

EID: 84904011362     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2014.0111     Document Type: Article

References (32)

1. Ekman VW. 1906 On dead water. The Norwegian North Polar Expedition, 1893-1896, Scientific Results 5, 1-152.
2. Mcphee MG, Kantha LH. 1989 Generation of internal wave by sea ice. J. Geophys. Res. 93, 3287-3302. (doi:10. 1029/JC094iC03p03287)
3. Schulkes RMSM, Hosking RJ, Sneyd AD. 1987 Wave due to a steadily moving source on a floating ice plate. Part 2. J. Fluid Mech. 180, 297-318. (doi:10. 1017/S0022112087001812)
4. Czipott PV, Levine MD, Paulson CA, Menemenlis D, Farmer DM, Williams RG. 1991 Ice flexural forced by internal wave packets in the Arctic Ocean. Science 254, 832-835. (doi:10. 1126/science. 254. 5033. 832)
5. Meiron DI, Saffman PG. 1983 Overhanging interfacial gravity waves of large amplitude. J. Fluid Mech. 129, 213-218. (doi:10. 1017/S0022112083000737)
6. Turner REL, Vanden-Broeck JM. 1988 Broadening of interfacial solitary waves. Phys. Fluids 31, 2486-2490. (doi:10. 1063/1. 866602)
7. P?ar?au EI, Vanden-Broeck JM, Cooker MJ. 2007 Nonlinear three-dimensional interfacial flows with a free surface. J. Fluid Mech. 591, 481-494.
8. P?ar?au EI, Vanden-Broeck JM. 2011 Three-dimensional waves beneath an ice sheet due to a steadily moving pressure. Phil. Trans. R. Soc. A 369, 2973-2988. (doi:10. 1098/rsta. 2011. 0115)
9. Milewski PA, Wang Z. 2013 Three dimensional flexural-gravity waves. Stud. Appl. Math. 131, 135-148. (doi:10. 1111/sapm. 12005)
10. Wang Z, Milewski PA, Vanden-Broeck JM. 2014 Computation of three-dimensional flexuralgravity solitary waves in arbitrary depth. Proc. IUTAM 11, 119-129. (doi:10. 1016/j. piutam. 2014. 01. 054)
11. Moni JN, King AC. 1995 Guided and unguided interfacial solitary waves. Q. J. Mech. Appl. Maths 48, 21-38. (doi:10. 1093/qjmam/48. 1. 21)
12. Michallet H, Dias F. 1999 Numerical study of generalized interfacial solitary waves. Phys. Fluids 11, 1502-1511. (doi:10. 1063/1. 870013)
13. P?ar?au EI, Dias F. 2001 Interfacial periodic waves of permanent form with free-surface boundary conditions. J. Fluid Mech. 437, 325-336.
14. Woolfenden HC, P?ar?au EI. 2011 Numerical computation of solitary waves in a two-layer fluid. J. Fluid Mech. 688, 528-550. (doi:10. 1017/jfm. 2011. 400)
15. Iooss G. 1999 Gravity and capillary-gravity periodic travelling waves for two superposed fluid layers, one being of infinite depth. J. Math. Fluid Mech. 1, 24-61. (doi:10. 1007/ s000210050003)
16. Dias F, Il'ichev A. 2001. Interfacial waves with free-surface boundary conditions: an approach via a model equation. Physica D 150, 278-300. (doi:10. 1016/S0167-2789(01)00149-X)
17. Fochesato C, Dias F, Grimshaw R. 2005 Generalized solitary waves and fronts in coupled Korteweg-de Vries systems. Physica D 210, 96-117. (doi:10. 1016/j. physd. 2005. 07. 010)
18. Craig W, Guyenne P, Kalisch H. 2005. Hamiltonian long wave expansions for free surfaces and interfaces. Commun. Pure Appl. Math. 58, 1587-1641. (doi:10. 1002/cpa. 20098)
19. Toland JF. 2008 Steady periodic hydroelastic waves. Arch. Ration. Mech. Anal. 189, 325-362. (doi:10. 1007/s00205-007-0104-2)
20. Squire VA, Hosking RJ, Kerr AD, Langhorne PJ. 1996 Moving loads on ice plate. Solid Mechanics and its Applications, vol. 45. Dordrecht, The Netherlands: Kluwer Academic Publishers.
21. Forbes LK. 1986 Surfacewaves of large amplitude beneath an elastic sheet. I. High-order series solution. J. Fluid Mech. 169, 409-428. (doi:10. 1017/S0022112086000708)
22. Vanden-Broeck JM. 1980 Numerical calculation of gravity-capillary interfacial waves of finite amplitude. Phys. Fluids 23, 1723-1726. (doi:10. 1063/1. 863197)
23. Laget O, Dias F. 1997 Numerical computation of capillary-gravity interfacial solitary waves. J. Fluid Mech. 349, 221-251. (doi:10. 1017/S0022112097006861)
24. Vanden-Broeck JM. 2010 Gravity-capillary free-surface flows. Cambridge, UK: Cambridge University Press.
25. Totz N, Wu SJ. 2012 A rigorous justification of the modulation approximation to the 2D full water wave problem. Commun. Math. Phys. 310, 817-882. (doi:10. 1007/s00220-012-1422-2)
26. Guyenne P, P?ar?au EI. 2012 Computations of fully nonlinear hydroelastic solitary wave on deep water. J. Fluid Mech. 713, 307-329. (doi:10. 1017/jfm. 2012. 458)
27. Dias F, Menasce D, Vanden-Broeck JM. 1996 Numerical study of capillary-gravity solitary waves. Eur. J. Mech. B 15, 17-36.
28. Wang Z, Vanden-Broeck JM, Milewski PA. 2013 Two-dimensional flexural-gravity waves of finite amplitude in deep water. IMA J. Appl. Math. 78, 750-761. (doi:10. 1093/imamat/hxt020)
29. Boonkasame A, Milewski PA. In press. A model for strongly nonlinear long interfacial waves with background shear. Stud. Appl. Math. (doi:10. 1111/sapm. 12036)
30. Benjamin TB. 1966 Internal waves of finite amplitude and permanent form. J. Fluid Mech. 25, 241-270. (doi:10. 1017/S0022112066001630)
31. Vanden-Broeck JM, P?ar?au EI. 2011 Two-dimensional generalized solitary waves and periodic waves under an ice sheet. Phil. Trans. R. Soc. A 369, 2957-2972. (doi:10. 1098/rsta. 2011. 0108)
32. Milewski PA, Vanden-Broeck JM, Wang Z. 2011 Hydroelastic solitary waves in deep water. J. Fluid Mech. 679, 628-640. (doi:10. 1017/jfm. 2011. 163)