Two-dimensional flexural-gravity waves of finite amplitude in deep water

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 78, Issue 4, 2013, Pages 750-761

  Wang, Z ^a   Vanden Broeck, J M ^a   Milewski, P A ^b  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b University of Bath   (United Kingdom)

Author keywords

elevation branch; flexural gravity; overhanging waves

Indexed keywords

CONTINUATION METHOD; ELEVATION BRANCH; FINITE AMPLITUDE; FLEXIBLE SHEETS; FLEXURAL-GRAVITY; FLEXURAL-GRAVITY WAVES; NUMERICAL SOLUTION; PSEUDOSPECTRAL METHODS;

CONFORMAL MAPPING; HYDROELASTICITY;

SOLITONS;

EID: 84880519771     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxt020     Document Type: Article

References (20)

1. Blyth, M. G., Pǎrǎu, E. I. & Vanden-Broeck, J.-M. (2011) Hydroelastic waves on fluid sheets. J. Fluid Mech., 689, 541-551.
2. Crapper, G. D. (1957) An exact solution for progressive capillary waves of arbitrary amplitude. J. Fluid Mech., 2, 532-540.
3. Dias, F., Menasce, D. & Vanden-Broeck, J.-M. (1996) Numerical study of capillary-gravity solitary waves. Eur. J. Mech. B Fluid, 15, 17-36.
4. Dyachenko, A. I., Kuznetsov, E. A., Spector, M. D. & Zakharov, V. E. (1996) Analytical description of the free surface dynamics of an ideal fluid (canonical formalism and conformal mapping). Phys. Lett. A, 221, 73-79.
5. Forbes, L. K. (1986) Surface waves of large amplitude beneath an elastic sheet. I. High-order series solution. J. Fluid Mech., 169, 409-428.
6. Forbes, L. K. (1988) Surface waves of large amplitude beneath an elastic sheet. II. Galerkin solution. J. Fluid Mech., 188, 491-508.
7. Guyenne, P. & Pǎrǎu, E. I. (2012) Computations of fully nonlinear hydroelastic solitary wave on deep water. J. Fluid Mech., 713, 307-329.
8. Hegarty, G. M. & Squire, V. A. (2002) Large amplitude periodic waves beneath an ice sheet. Ice in the Environment. Proc. 16th IAHR Int. Symp. on Ice (V. A. Squire & P. J. Langhorne eds), vol. 2. Madrid, Spain: International Association of Hydraulic Engineering and Research, pp. 310-317.
9. Milewski, P. A., Vanden-Broeck, J.-M. & Wang, Z. (2011) Hydroelastic solitary waves in deep water. J. Fluid Mech., 679, 628-640.
10. Milewski, P. A., Vanden-Broeck, J.-M. &Wang, Z. (2012) Steady dark solitary flexural gravity waves. Proc. R. Soc. A, 469 (2150), 20120085, doi:10.1098/rspa.2012.0485.
11. Milewski, P. A. & Wang, Z. (2013) Three dimensional flexural-gravity waves. Stud. Appl. Math., (in press) DOI: 10.1111/sapm.12005.
12. Pǎrǎu, E. I. & Dias, F. (2002) Nonlinear effects in the response of a floating ice plate to a moving load. J. Fluid Mech., 460, 281-305.
13. Plotnikov, P. I. & Toland, J. F. (2011) Modelling nonlinear hydroelastic waves. Philos. Trans. R. Soc. Lond. A, 369, 2942-2956.
14. Squire, V. A., Hosking, R. J., Kerr, A. D. & Langhorne, P. J. (1996) Moving Loads on Ice Plates. Solid Mechanics and its Applications. Dordrecht: Kluwer.
15. Toland, J. F. (2008) Steady periodic hydroelastic waves. Arch. Ration. Mech. Anal., 189, 325-362.
16. Vanden-Broeck, J.-M. (2010) Gravity-Capillary Free-Surface Flows. Cambridge: Cambridge University Press.
17. Vanden-Broeck, J.-M. & Dias, F. (1992) Gravity-capillary solitary waves in water of infinite depth and related free-surface flows. J. Fluid Mech., 240, 549-557.
18. Vanden-Broeck, J.-M. & Pǎrǎu, E. I. (2011) Two-dimensional generalized solitary waves and periodic waves under an ice sheet. Philos. Trans. R. Soc. Lond. A, 369, 2957-2972.
19. Wilson, J. T. (1958) Moving loads on floating ice sheets. University of Michigan Research Institute (UMRI Project 2432).
20. Wilton, J. R. (1915) On ripples. Philos. Mag., 29, 688-700.