Computation of three-dimensional flexural-gravity solitary waves in arbitrary depth

Procedia IUTAM

Volumn 11, Issue , 2014, Pages 119-129

  Wang, Zhan ^a   Milewski, Paul A ^b   Vanden Broeck, Jean Marc ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b University of Bath   (United Kingdom)

Author keywords

Flexural gravity waves; Solitary waves; Water waves

Indexed keywords

WATER WAVES; WAVEFORM ANALYSIS;

CONTINUATION METHOD; ELASTIC SHEETS; FINITE AMPLITUDE; FLEXURAL-GRAVITY WAVES; FLUID EQUATIONS; SHALLOW WATERS; SMALL AMPLITUDE; WEAKLY NON-LINEAR;

SOLITONS;

EID: 84894134645     PISSN: None     EISSN: 22109838     Source Type: Conference Proceeding    
DOI: 10.1016/j.piutam.2014.01.054     Document Type: Conference Paper

References (18)

1. Craig W, Nicholls DP. Traveling gravity water waves in two and three dimensions. Euro../. Mech. B/Fluids 2(X)2: 21: 615-641.
2. Craig W, Sulem C. Numerical simulation of gravity waves. J. Cotnp. Phys. 1993; 108: 73-83.
3. Guyenne P. PMu EL Computations of fully nonlinear hydroelastic solitary wave on deep water. J. Fluid Mech. 2012: 713: 307-329.
4. Guyenne P. Parftu EL Finite-depth effects on solitary waves in a floating ice sheet. Submitted.
5. Milewski PA. Vanden-Broeck JM, Wang Z. Hydroelastic solitary waves in deep water. J. Fluid Mech. 2011; 679: 628-640.
6. Milewski PA, Wang Z. Three dimensional flexural-gravity waves. Stud. Appl. Math. 2013; doi: 10.111 l/sapm.l2(X)5.
7. Nicholls DP. Reitich F. Stability of high-order methods for the computation of Dirichlet-Neumann operator. J. Cotnp. Phys. 2001; 170: 276-298.
8. Pdritu EL, Dias F. Nonlinear effects in the response of a floating ice plate to a moving load. J. Fluid Mech. 2002; 460: 281-305.
9. P̌ařau EL, Vanden-Broeck JM. Three-dimensional waves beneath an ice sheet due to a steadily moving pressure. Phil. Trans. K. Soc. A 2011: 369: 2973-2988.
10. P̌ařau EI, Vanden-Broeck JM. Three-dimensional nonlinear waves under an ice sheet and related flows. In Proc. of the 21th Int. Offshore and Polar Eng. Conf. (ISOPE), Maui, Hawaii, 19-24 June 2011. Mountain View, CA: ISOPE.
11. P̌ařau EI, Vanden-Broeck JM, Cooker MJ. Nonlinear three-dimensional gravity-capillary solitary waves. J. Fluid Mech. 2005; 536: 99-105.
12. Plotnikov PI, Toland JF. Modelling nonlinear hydroelastic waves. Phil. Trans. R. Soc. Lond. A 2011; 369: 2942-2956.
13. Squire VA, Hosking RJ, Kerr AD, Langhorne PJ. Moving Loads on Ice Plates. (Solid Mechanics and Its Applications). Kluwer; 1999.
14. Sulem C, Sulem PL. The nonlinear Schr̈ordinger equation: self-focusing and wave collapse. Applied Mathematical Sciences, Vol. 139, Springer-Verlag, New York; 1999.
15. Wang Z, Milewski PA. Dynamics of gravity-capillary solitary waves in deep water. J. Fluid Mech. 2012; 708: 480-501.
16. Wang Z, Vanden-Broeck JM, Milewski PA. Two-dimensional flexural-gravity waves of finite amplitude in deep water. IMA J. Appl. Math. 2013; doi:10.1093/imamat/hxt020.
17. Xu L, Guyenne P. Numerical simulation of three-dimensional nonlinear water waves. J. Comp. Phys. 2009; 228: 8446-8466.
18. Zakharov VE. Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 1968; 2: 190-194.