Asymptotic modeling and numerical simulation of solitary waves in a floating ice sheet

Proceedings of the International Offshore and Polar Engineering Conference

Volumn 2015-January, Issue , 2015, Pages 467-475

  Guyenne, Philippe ^a   Pərəu, Emilian I ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b UNIVERSITY OF EAST ANGLIA   (United Kingdom)

Author keywords

Boussinesq models; Flexural gravity waves; Hamilto nian systems; High order spectral method; Sea ice; Solitary waves

Indexed keywords

GLACIERS; GRAVITY WAVES; NUMERICAL MODELS; SEA ICE; SOLITONS;

BOUSSINESQ MODEL; FLEXURAL-GRAVITY WAVES; GOVERNING EQUATIONS; HAMILTONIAN FORMULATIONS; HIGH-ORDER SPECTRAL METHOD; MODEL PREDICTION; THREE-DIMENSIONAL SETTINGS; WEAKLY NON-LINEAR;

ICE;

EID: 84944679924     PISSN: 10986189     EISSN: 15551792     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (32)

1. Biondini, G, and Chakravarty, S (2006). "Soliton solutions of the Kadomtsev-Petviashvili II equation," J Math Phys, 47, 033514.
2. Bonnefoy, F, Meylan, MH, and Ferrant, P (2009). "Nonlinear higherorder spectral solution for a two-dimensional moving load on ice," J Fluid Mech, 621, 215-242.
3. Champneys, AR, Vanden-Broeck, J-M, and Lord, GJ (2002). "Do true elevation gravity-capillary solitary waves exist? A numerical investigation," J Fluid Mech, 454, 403-417.
4. Craig, W, and Groves, MD (1994). "Hamiltonian long-wave approximations to the water-wave problem," Wave Motion, 19, 367-389.
5. Craig, W, Guyenne, P, and Kalisch, H (2005a). "Hamiltonian long wave expansions for free surfaces and interfaces," Comm Pure Appl Math, 58, 1587-1641.
6. Craig, W, Guyenne, P, Nicholls, DP, and Sulem, C (2005b). "Hamiltonian long wave expansions for water waves over a rough bottom," Proc R Soc Lond Ser A Math Phys Eng Sci, 461, 839-873.
7. Craig, W, Guyenne, P, and Sulem, C (2012). "The surface signature of internal waves," J Fluid Mech, 710, 277-303.
8. Craig, W, Schanz, U, and Sulem, C (1997). "The modulation regime of three-dimensional water waves and the Davey-Stewartson system," Ann Inst Henri Poincar� Anal Non Lin�aire, 14, 615-667.
9. Craig, W, and Sulem, C (1993). "Numerical simulation of gravity waves," J Comp Phys, 108, 73-83.
10. Forbes, LK (1986). "Surface-waves of large amplitude beneath an elastic sheet. Part 1. High-order solutions," J Fluid Mech, 169, 409-428.
11. Guyenne, P, and Nicholls, DP (2007). "A high-order spectral method for nonlinear water waves over moving bottom topography," SIAM J Sci Comp, 30, 81-101.
12. Guyenne, P, and Pərəu, EI (2012). "Computations of fully nonlinear hy-droelastic solitary waves on deep water," J Fluid Mech, 713, 307-329.
13. Guyenne, P, and Pərəu, EI (2014). "Finite-depth effects on solitary waves in a floating ice sheet," J Fluids Struct, 49, 242-262.
14. Haragus-Courcelle, M, and Ilichev, A (1998). "Three-dimensional solitary waves in the presence of additional surface effects," Eur J Mech B/Fluids, 17, 739-768.
15. Hegarty, GM, and Squire, VA (2008). "A boundary-integral method for the interaction of large-amplitude ocean waves with a compliant floating raft such as a sea-ice floe," J Eng Math, 62, 355-372.
16. Kaup, DJ (1975). "A higher-order wave equation and the method for solving it," Prog Theor Phys, 54, 396-408.
17. Kohout, AL, Williams, MJM, Dean, SM, and Meylan, MH (2014). "Storm-induced sea-ice breakup and the implications for ice extent," Nature, 509, 604-607.
18. Korobkin, A, Pərəu, EI, and Vanden-Broeck, J-M (2011). "The mathematical challenges and modelling of hydroelasticity," Phil Trans R Soc A, 369, 2803-2812.
19. Longuet-Higgins, MS (1989). "Capillary-gravity waves of solitary type on deep water," J Fluid Mech, 200, 451-470.
20. Marko, JR (2003). "Observations and analyses of an intense waves-in-ice event in the Sea of Okhotsk," J Geophys Res, 108, 3296.
21. Michallet, H, and Dias, F (1999). "Numerical study of generalized interfacial solitary waves," Phys Fluids, 11, 1502-1511.
22. Milewski, PA, Vanden-Broeck, J-M, and Wang, Z (2011). "Hydroelastic solitary waves in deep water," J Fluid Mech, 679, 628-640.
23. Milewski, PA, and Wang, Z (2013). "Three dimensional flexural-gravity waves," Stud Appl Math, 131, 135-148.
24. Pərəu, E, and Dias, F (2002). "Nonlinear effects in the response of a floating ice plate to a moving load," J Fluid Mech, 460, 281-305.
25. Pərəu, EI, and Vanden-Broeck, J-M (2011). "Three-dimensional waves beneath an ice sheet due to a steadily moving pressure," Phil Trans R Soc A, 369, 2973-2988.
26. Plotnikov, PI, and Toland, JF (2011). "Modelling nonlinear hydroelas-tic waves," Phil Trans R Soc A, 369, 2942-2956.
27. Squire, VA (2011). "Past, present and impendent hydroelastic challenges in the polar and subpolar seas," Phil Trans R Soc A, 369, 2813-2831.
28. Squire, VA, Hosking, RJ, Kerr, AD, and Langhorne, PJ (1996). Moving Loads on Ice Plates, Kluwer, 45.
29. Takizawa, T (1985). "Deflection of a floating sea ice sheet induced by a moving load," Cold Reg Sci Tech, 11, 171-180.
30. Xia, X, and Shen, HT (2002). "Nonlinear interaction of ice cover with shallow water waves in channels," J Fluid Mech, 467, 259-268.
31. Xu, L, and Guyenne, P (2009). "Numerical simulation of three-dimensional nonlinear water waves," J Comp Phys, 228, 8446-8466.
32. 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.