Numerical computation of solitary waves in a two-layer fluid

Journal of Fluid Mechanics

Volumn 688, Issue , 2011, Pages 528-550

  Woolfenden, H C ^a   Parau E I ^a  

^a UNIVERSITY OF EAST ANGLIA   (United Kingdom)

Author keywords

capillary waves; solitary waves

Indexed keywords

FROUDE NUMBER; SURFACE TENSION;

BOUNDARY INTEGRAL METHODS; CAPILLARY WAVE; CAUCHY INTEGRAL FORMULA; DISPERSION RELATIONS; NUMERICAL COMPUTATIONS; SOLI-TARY WAVE SOLUTIONS; TWO-DIMENSIONAL FLOW; WAVES ON THE INTERFACES;

SOLITONS;

CAPILLARY WAVE; FROUDE NUMBER; INTERFACE; PARAMETERIZATION; SOLITARY WAVE; SPECTRAL ANALYSIS; STEADY FLOW; TWO-DIMENSIONAL FLOW;

EID: 84855513492     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2011.400     Document Type: Article

References (46)

1. AKYLAS, T. J. & GRIMSHAW, R. H. J. 1992 Solitary internal waves with oscillatory tails. J. Fluid Mech. 242, 279-298.
2. BAINES, P. G. 1995 Topographic Effects in Stratified Flows. Cambridge University Press.
3. BARRANDON, M. & IOOSS, G. 2005 Water waves as a spatial dynamical system; infinite depth case. Chaos 15, 037112.
4. BENJAMIN, T. B. 1966 Internal waves of finite amplitude and permanent form. J. Fluid Mech. 25, 241-270.
5. BENJAMIN, T. B. 1967 Internal waves of permanent form in fluids of great depth. J. Fluid Mech. 29 (03), 559-592.
6. BENJAMIN, T. B. 1992 A new kind of solitary wave. J. Fluid Mech. 245, 401-411.
7. CALVO, D. C. & AKYLAS, T. R. 2003 On interfacial gravity-capillary solitary waves of the Benjamin type and their stability. Phys. Fluids 15, 1261-1270. (Pubitemid 36751505)
8. CAMASSA, R., CHOI, W., MICHALLET, H., RUSAS, P.-O. & SVEEN, J. D. 2006 On the realm of validity of strongly nonlinear asymptotic approximations for internal waves. J. Fluid Mech. 549, 1-23.
9. CHOI, W. & CAMASSA, R. 1996 Weakly nonlinear internal waves in a two-fluid system. J. Fluid Mech. 313, 83-103. (Pubitemid 126467081)
10. CHOI, W. & CAMASSA, R. 1999 Fully nonlinear internal waves in a two-fluid system. J. Fluid Mech. 396, 1-36. (Pubitemid 129657785)
11. CRAIG, W., GUYENNE, P. & KALISCH, H. 2005 Hamiltonian long-wave expansions for free surfaces and interfaces. Commun. Pure Appl. Maths 58, 1587-1641. (Pubitemid 43082564)
12. DIAS, F. & IL'ICHEV, A. 2001 Interfacial waves with free-surface boundary conditions: an approach via a model equation. Physica D 150 (3-4), 278-300. (Pubitemid 32265315)
13. DIAS, F. & IOOSS, G. 1996 Capillary-gravity interfacial waves in infinite depth. Eur. J. Mech. (B/Fluids) 15, 367-393.
14. EKMAN, V. W. 1904 On dead water. Norwegian North Polar Expedition, 1893-1896, Scientific Results 5, 1-150.
15. EVANS, W. A. B. & FORD, M. J. 1996 An integral equation approach to internal (2-layer) solitary waves. Phys. Fluids 8, 2032-2047.
16. FARMER, D. M. & DUNGAN SMITH, J. 1980 Tidal interaction of stratified flow with a sill in Knight Inlet. Deep-Sea Res. A. Oceanogr. Res. Papers 27 (3-4), 239-246.
17. FOCHESATO, C., DIAS, F. & GRIMSHAW, R. 2005 Generalized solitary waves and fronts in coupled Korteweg-de Vries systems. Physica D 210, 96-117. (Pubitemid 41277025)
18. FORBES L. K. & HOCKING, G. C. 2006 An intrusion layer in stationary incompressible fluids. Part 2. A solitary wave. Eur. J. Appl. Maths 17 05 577-595.
19. FORBES L. K., HOCKING, G. C. & FARROW, D. E. 2006 An intrusion layer in stationary incompressible fluids. Part 1. Periodic waves. Eur. J. Appl. Maths 17 05 557-575.
20. FRUCTUS, D. & GRUE, J. 2004 Fully nonlinear solitary waves in a layered stratified fluid. J. Fluid Mech. 505, 323-347. (Pubitemid 38673044)
21. GRIMSHAW, R. & CHRISTODOULIDES, P. 2008 Gap-solitons in a three-layered stratified flow. Wave Motion 45 (6), 758-769.
22. HAUT, T. S. & ABLOWITZ, M. J. 2009 A reformulation and applications of interfacial fluids with a free surface. J. Fluid Mech. 631, 375-396.
23. HELFRICH, K. R. & MELVILLE, W. K. 2006 Long nonlinear internal waves. Annu. Rev. Fluid Mech. 38, 395-425. (Pubitemid 43240182)
24. IOOSS, G. 1999 Gravity and capillary-gravity periodic travelling waves for two superposed fluid layers, one being of infinite depth. J. Math. Fluid Mech. 1, 24-61.
25. IOOSS, G., LOMBARDI, E. & SUN, S. M. 2002 Gravity travelling waves for two superposed fluid layers, one being of infinite depth: a new type of bifurcation. Phil. Trans. R. Soc. Lond. A 360, 2245-2336.
26. JOSEPH, R. I. 1977 Solitary waves in a finite depth fluid. J. Phys. A 10, L225-L227.
27. KAKUTANI, T. & YAMASAKI, N. 1978 Solitary waves on a two-layer fluid. J. Phys. Soc. Japan 45, 674-679.
28. KIM, B. & AKYLAS, T. R. 2006 On gravity-capillary lumps. Part 2 Two-dimensional Benjamin equation. J. Fluid Mech. 557, 237-256. (Pubitemid 44069747)
29. LAGET, O. & DIAS, F. 1997 Numerical computation of capillary-gravity interfacial solitary waves. J. Fluid Mech. 349, 221-251. (Pubitemid 127475556)
30. LAMB, K. G. 2000 Conjugate flows for a three-layer fluid. Phys. Fluids 12, 2169-2185.
31. LOMBARDI, E. & IOOSS, G. 2003 Gravity solitary waves with polynomial decay to exponentially small ripples at infinity. Ann. Inst. Henri Poincare C. Non-Linear Anal. 20, 669-704.
32. MERCIER, M. J., VASSEUR, R. & DAUXOIS, T. 2011 Resurrecting dead-water phenomenon. Nonlin. Process. Geophys. 18, 193-208.
33. MICHALLET, H. & BARTHELEMY, E. 1998 Experimental study of interfacial solitary waves. J. Fluid Mech. 366, 159-177. (Pubitemid 128488653)
34. MICHALLET, H. & DIAS, F. 1999 Numerical study of generalized interfacial solitary waves. Phys. Fluids 11, 1502.
35. MONI, J. N. & KING, A. C. 1995 Guided and unguided interfacial solitary waves. Q. J. Mech. Appl. Maths 48 (1), 21.
36. ONO, H. 1975 Algebraic solitary waves in stratified fluids. J. Phys. Soc. Japan 39 (4), 1082-1091.
37. OSBORNE, A. R., BURCH, T. L. & SCARLET, R. I. 1978 The influence of internal waves on deep-water drilling. J. Petrol. Tech. 30 (10), 1497-1504. (Pubitemid 9392187)
38. PARA U, E. 2000 Ondes interfaciales de flexion-gravit́e et de capillarit́e-gravit́e. PhD thesis, Univ. de Nice Sophia Antipolis, and West Univ. of Timisoara.
39. PARA U, E. & DIAS, F. 2001 Interfacial periodic waves of permanent form with free-surface boundary conditions. J. Fluid Mech. 437, 325-336. (Pubitemid 32596307)
40. PARAU, E. & SASU, B. 1996 Surface-interface solitary waves. Semin. Math. Anal. Appl. 72, 1-11.
41. PARAU, E. I., VANDEN-BROECK, J.-M. & COOKER, M. J. 2007 Nonlinear three-dimensional interfacial flows with a free surface. J. Fluid Mech. 591, 481-494.
42. PETERS, A. S. & STOKER, J. J. 1960 Solitary waves in liquid having non-constant density. Commun. Pure Appl. Maths 13, 115-164.
43. PHILLIPS, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
44. RUS°A S, P.-O. & GRUE, J. 2002 Solitary waves and conjugate flows in a three-layer fluid. Eur. J. Mech. (B/Fluids) 21, 185-206. (Pubitemid 34288302)
45. TURNER, R. E. L. & VANDEN-BROECK, J.-M. 1988 Broadening of interfacial solitary waves. Phys. Fluids 31, 2486-2490.
46. VANDEN-BROECK, J.-M. 2010 Gravity Capillary Free-Surface Flows. Cambridge University Press.