Reflection of a high-amplitude solitary wave at a vertical wall

Journal of Fluid Mechanics

Volumn 342, Issue , 1997, Pages 141-158

  Cooker, M J ^a   Weidman, P D ^b   Bale, D S ^c  

^a UNIVERSITY OF EAST ANGLIA   (United Kingdom)

^b UCB 450   (United States)

^c UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; INTEGRAL EQUATIONS; PERTURBATION TECHNIQUES; REFLECTION;

BOUNDARY INTEGRAL METHOD; EULER EQUATIONS; SOLITARY WAVE REFLECTION;

WATER WAVES;

REFLECTION; WALL; WAVE;

REFLECTION; SOLITARY WAVES; WALL;

EID: 0031177684     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S002211209700551X     Document Type: Article

References (23)

1. BAKER, G. R., MEIRON, D. I. & ORSZAG, S. A. 1982 Generalised vortex methods for free-surface flow problems. J. Fluid Mech. 123, 477-501.
2. BYATT-SMITH, J. G. B. 1971 An integral equation for unsteady surface waves and a comment on the Boussinesq equation. J. Fluid Mech. 49, 625-633.
3. BYATT-SMITH, J. G. B. 1988 The reflection of a solitary wave by a vertical wall. J. Fluid Mech. 197, 503-521.
4. CHAN, R. K. C. & STREET, R. L. 1970 A computer study of finite amplitude water waves. J. Comput. Phys. 6, 68-94.
5. COOKER, M. J. 1990 The interaction between steep water waves and coastal structures. PhD thesis, University of Bristol, UK.
6. DOLD, J. W. 1992 An efficient surface-integral algorithm applied to unsteady gravity waves. J. Comput. Phys. 103, 90-115.
7. DOLD, J. W. & PEREGRINE, D. H. 1986 An efficient boundary-integral method for steep unsteady water waves. In Numerical Methods for Fluid Dynamics II (ed. K. W. Morton & M. J. Baines), pp. 671-679. Oxford University Press.
8. FENTON, J. D. & RIENECKER, M. M. 1982 A Fourier method for solving nonlinear water-wave problems: application to solitary-wave interactions. J. Fluid Mech. 118, 411-443.
9. GRILLI, S. & SVENDSEN, I. A. 1990 The propagation and runup of solitary waves on steep slopes. CACR Rep. 91-04. Department of Civil Engineering. University of Delaware.
10. LONGUET-HIGGINS, M. S. & GOKELET, E. D. 1976 The deformation of steep surface waves on water. I. A numerical method of computation. Proc. R. Soc. Lond. A 350, 1-26.
11. MAXWORTHY, T. 1976 Experiments on the collision between two solitary waves. J. Fluid Mech. 76, 177-185.
12. MIRIE, R. M. & SU, C. H. 1982 Collisions between two solitary waves. J. Fluid Mech. 115, 475-492.
13. OIKAWA, M. & YAJIMA, N. 1973 Interaction of solitary waves - a perturbation approach to nonlinear systems. J. Phys. Soc. Japan 34, 1093-1099.
14. POWER, H. & CHWANG, A. T. 1984 On reflection of a planar solitary wave. Wave Motion 6, 183-195.
15. RENOUARD, D. P., SEABRA-SANTOS, F. J. & TEMPERVILLE, A. M. 1985 Experimental study of the generation, damping and reflexion of a solitary wave. Dyn. Atmos. Oceans 9, 341-358.
16. SEGUR, H. 1973 The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1. J. Fluid Mech. 59, 721-736.
17. SU, C. H. & GARDNER, C. S. 1969 Korteweg-de Vries equation and generalizations. III. Derivation of the Korteweg-de Vries equation and Burgers equation. J. Math. Phys. 10, 536-539.
18. SU, C. H. & MIRIE, R. M. 1980 On head-on collisions between two solitary waves. J. Fluid. Mech. 98, 509-525 (referred to herein as SM).
19. TANAKA, M. 1986 The stability of solitary waves. Phys. Fluids 29, 650-655.
20. TANAKA, M., DOLD, J. W., LEWY, M. & PEREGRINE, D. H. 1987 Instability and breaking of a solitary wave. J. Fluid Mech. 185, 235-248.
21. TEMPERVILLE, A. 1979 Interactions of solitary waves in shallow water theory. Arch. Mech. 31, 177-184.
22. VINJE, T. & BREVIK, P. 1981 Numerical simulation of breaking waves. Adv. Water Resources 4, 77-82.
23. ZABUSKY, N. J. & KRUSKAL, M. D. 1965 Interaction of 'solitons' in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15, 240-243.