Three-dimensional gravity-capillary solitary waves in water of finite depth and related problems

Physics of Fluids

Volumn 17, Issue 12, 2005, Pages 1-9

  Parau E I ^a   Vanden Broeck, J M ^a   Cooker, M J ^a  

^a UNIVERSITY OF EAST ANGLIA   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CAPILLARY FLOW; GRAVITY WAVES; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; SURFACE TENSION;

BOND NUMBER; BOUNDARY INTEGRAL EQUATION METHOD; GRAVITY CAPILLARY WAVES;

WATER WAVES;

BIFURCATION (MATHEMATICS); CAPILLARY FLOW; GRAVITY WAVES; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; SURFACE TENSION; WATER WAVES;

EID: 31144445710     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2140020     Document Type: Article

References (19)

1. D. J. Korteweg and G. de Vries, "On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves," Philos. Mag. PHMAA40031-8086 36, 422 (1895).
2. J. K. Hunter and J.-M. Vanden-Broeck, "Solitary and periodic gravity-capillary waves of finite amplitude," J. Fluid Mech. JFLSA70022-1120 134, 205 (1983).
3. A. R. Champneys, J.-M. Vanden-Broeck, and G. J. Lord, "Do true elevation gravity-capillary solitary waves exist? A numerical investigation," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112002008984 454, 403 (2002).
4. F. Dias and G. Iooss, "Water-waves as a spatial dynamical system," in Handbook of Mathematical Fluid Dynamics (Elsevier, Amsterdam, 2003), Vol. 2, p. 443.
5. J.-M. Vanden-Broeck and F. Dias, "Gravity-capillary solitary waves in water of infinite depth and related free-surface flows," J. Fluid Mech. JFLSA70022-1120 240, 549 (1992).
6. F. Dias and G. Iooss, "Capillary-gravity solitary waves with damped oscillations," Physica D PDNPDT0167-278910.1016/ 0167-2789(93)90064-8 65, 399 (1993).
7. F. Dias, D. Menasce, and J.-M. Vanden-Broeck, "Numerical study of capillary-gravity solitary waves," Eur. J. Mech. B/Fluids EJBFEV0997-7546 15, 17 (1996).
8. E. Pǎrǎu, J.-M. Vanden-Broeck, and M. Cooker, "Nonlinear three dimensional gravity-capillary solitary waves and related free-surface flows," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112005005136 536, 99 (2005).
9. B. Kim and T. R. Akylas, "On gravity-capillary lumps," J. Fluid Mech. JFLSA70022-1120 540, 337 (2005).
10. P. A. Milewski, "Thee-dimensional localized solitary gravity-capillary waves," Commun. Math. Sci. ZZZZZZ1539-6746 3, 89 (2005).
11. H. Lamb, Hydrodynamics, 6th ed. (Cambridge University Press, Cambridge, 1932).
12. J. W. Wehausen and E. V. Laitone, "Surface waves," in Encyclopaedia of Physics Vol. IX (Springer, Berlin, 1960), p. 446.
13. G. Iooss and K. Kirchgässner, "Water waves for small surface tension: An approach via normal form," Proc. - R. Soc. Edinburgh, Sect. A: Math. PEAMDU0308-2105 122, 267 (1992).
14. B. B. Kadomtsev and V. I. Petviashvili, "On the stability of solitary waves in weakly dispersing media," Sov. Phys. Dokl. SPHDA90038-5689 15, 539 (1970).
15. L. K. Forbes, "An algorithm for 3-dimensional free-surface problems in hydrodynamics," J. Comput. Phys. JCTPAH0021-999110.1016/ 0021-9991(89)90052-1 82, 330 (1989).
16. E. Pǎrǎu and J.-M. Vanden-Broeck, "Nonlinear two- and three-dimensional free surface flows due to moving disturbances," Eur. J. Mech. B/Fluids EJBFEV0997-754610.1016/S0997-7546(02)01212-8 21, 643 (2002).
17. G. C. Hocking, J.-M. Vanden-Broeck, and L. K. Forbes, "A note on withdrawal from a fluid of finite depth through a point sink," ANZIAM J. ZZZZZZ1445-8735 44, 181 (2002).
18. E. Raphäel and P.-G. de Gennes, "Capillary gravity waves caused by a moving disturbance. Wave resistance," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.53.3448 53, 3448 (1996).
19. S.-M. Sun and J. B. Keller,"Capillary-gravity wave drag," Phys. Fluids PHFLE61070-663110.1063/1.1384889 13, 2146 (2001).