Fully nonlinear solitary waves in a layered stratified fluid

Journal of Fluid Mechanics

Volumn 505, Issue , 2004, Pages 323-347

  Fructus, Dorian ^a   Grue, John ^a  

^a UNIVERSITY OF OSLO   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

GREEN'S FUNCTION; MATHEMATICAL MODELS; NATURAL FREQUENCIES; SHOCK WAVES; THERMAL STRATIFICATION;

HELMHOLTZ EQUATION; SOLITARY WAVES; STREAM FUNCTIONS;

FLUID MECHANICS;

FLUID FLOW; MATHEMATICAL ANALYSIS; MODEL; STRATIFIED FLUID; WAVE;

EID: 2442668785     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112004008596     Document Type: Article

References (42)

1. AMICK, C. J. & TURNER, R. E. L. 1986 A global theory of internal solitary waves in two-fluid systems. Trans. Am. Math. Soc. 298, 431.
2. BOGUCKI, D. & GARRETT, C. 1993 A simple model for the shear-induced decay of an internal solitary wave. J. Phys. Oceanogr. 23, 1767.
3. BROWAND, F. K. & WANG, Y. H. 1972 An experiment on the growth of small disturbances at the interface between two streams of different densities and velocities. Proc. Intl Symp. Stratified Flows, Aug 29-31. Novosibirsk, U.S.S.R. ASCE.
4. BROWN, D. J. & CHRISTIE, D. R. 1998 Fully nonlinear solitary waves in continuously stratified incompressible boussinesq fluids Phys. Fluids 10, 2569.
5. CASTRO, I. P., SNYDER, W. H. & MARSH, G. L. 1983 Stratified flow over three-dimensional ridges. J. Fluid Mech. 135, 261.
6. DAVIES, R. E. & ACRIVOS, A. 1967 The stability of oscillatory internal waves. J. Fluid Mech. 30, 723.
7. DELISI, D. P. & ORLANSKI, I. 1975 On the role of density jumps in the reflexion and breaking of internal gravity waves. J. Fluid Mech. 69, 445.
8. DERZHO, O. G. & GRIMSHAW, R. 1997 Solitary waves with a vortex core in a shallow layer of stratified fluid. Phys. Fluids 9, 11.
9. DRAZIN, P. G. 1977 On the instability of and internal gravity wave. Proc. R. Soc. Lond. A 356, 411.
10. DUBREIL-JACOTIN, L. 1932 Sur les ondes type permanent dans les liquides heterogenes. Atti dela Reale Academic Nationale dei Lincei. 15(6), 44.
11. ELIASSEN, A. & FJsRTOFT, R. 1992 The interface method for calculating the temporal evolution of a two-fluid system. Frontiers of Science, Ann. NY Acad. Sci. 661, 54.
12. EVANS, W. A. B. & FORD, M. J. 1996 An integral equation approach to internal (2-layer) solitary waves. Phys. Fluids 8, 2032.
13. GRUE, J., FRIIS, A., PALM, E. & RUSÅS, P.-O. 1997 A method for computing unsteady fully nonlinear interfacial waves. J. Fluid Mech. 351, 223.
14. GRUE, J., JENSEN, A., RUSÅS, P.-O. & SVEEN, J. K. 1999 Properties of large amplitude internal waves. J. Fluid Mech. 380, 257.
15. GRUE, J., JENSEN, A., RUSÅS, P.-O. & SVEEN, J. K. 2000 Breaking and broadening of internal solitary waves. J. Fluid Mech. 413, 181.
16. GRUE, J. & OSTROVSKY, L. A. 2002 Analytical models and fully nonlinear computations of strongly nonlinear internal solitons. Abstracts. European Geophy. Soc., Nice, April 2002.
17. HAZEL, P. 1972 Numerical studies of the stability of inviscid stratified shear flows. J. Fluid Mech. 51, 39.
18. HOLMBOE, J. 1962 On the behaviour of symmetric waves in stratified shear layers. Geophys. Publ. (In memory of Vilhelm Bjerknes) 24, 67.
19. HUTHNANCE, J. M. 1989 Internal tides and waves near the continental shelf edge. Geophys. Astrophys. Fluid Dyn. 48, 81.
20. KLOSTERMEYER, J. 1982 On parametric instabilities of finite-amplitude internal gravity waves. J. Fluid Mech. 119, 367.
21. LAMB, G. K. 1994 Numerical simulations of stratified inviscid flow over a smooth obstacle. J. Fluid Mech. 260, 1.
22. LAMB, G. K. 2002 A numerical investigation of solitary internal waves with trapped cores formed via shoaling. J. Fluid Mech. 451, 109.
23. LAMB, G. K. 2003 Shoaling solitary internal waves: on a criterion for the formation of waves with trapped core. J. Fluid Mech. 478, 81.
24. LONG, R. R. 1958 Tractable models of steady-state stratified flow with shear. Q. J. R. Met. Soc. 84, 159.
25. MAJDA, A. J. & SHEFTER, M. G. 1998 Elementary stratified flows with instability at large Richardson number. J. Fluid Mech. 376, 319.
26. MCEVAN, A. D. & ROBINSON, R. M. 1975 Parametric instability of internal gravity waves. J. Fluid Mech. 67, 667.
27. MIED, R. P. 1976 The occurrence of parametric instabilities in finite-amplitude internal gravity waves. J. Fluid Mech. 78, 763.
28. ORLANSKI, I. & BRYAN, K. 1969 Formation of the thermocline step structure by large-amplitude internal gravity waves. J. Geophys. Res. 74, 6975.
29. OSTROVSKY, L. A. & GRUE, J. 2003 Evolution equations for strongly nonlinear internal waves. Phys. Fluids 15, 10.
30. OSTROVSKY, L. A. & STEPANYANTS, YU, A. 1989 Do internal solitons exist in the ocean? Rev. Geophys. 27, 293.
31. PELINOVSKY, E., POLOUKHINA, O. & LAMB, K. 2000 Nonlinear internal waves in the ocean stratified in density and flow. Oceanology 40, N. 5, 805-815.
32. PULLIN, D. I. & GRIMSHAW, R. H. J. 1988 Finite-amplitude solitary waves at the interface between two homogeneous fluids. Phys. Fluids 31, 3550.
33. RUSÅS, P.-O. & GRUE, J. 2002 Solitary waves and conjugate flows in a three-layer fluid. Eur. J. Mech. B/Fluids 21, 185-206.
34. SCOTTI, R. S. & CORCOS, G. M. 1972 An experiment on the stability of small disturbances in a stratified free shear layer. J. Fluid Mech. 52, 499.
35. STASTNA, M. & LAMB, K. G. 2002 Large fully nonlinear internal solitary waves: The effect of background current. Phys. Fluids 14, 2987.
36. STANTON, T. P. & OSTROVSKY, L. A. 1998 Observations of highly nonlinear internal solitons over the continental shelf. Geophys. Rev. Lett. 25, 2695.
37. TUNG, K.-K., CHAN, T. F. & KUBOTA, T. 1982 Large amplitude internal waves of permanent form. Stud. Appl. Maths 66, 1.
38. TURKINGTON, B., EYDELAND, A. & WANG, S. 1991 A computational method for solitary internal waves in a continuously stratified fluid. Stud. Appl. Maths 85, 93.
39. TURNER, R. E. L. & VANDEN-BROECK, J.-M. 1988 Broadening of interfacial solitary waves. Phys. Fluids 31, 2486.
40. VORONOVICH, A. G. 2003 Strong solitary internal waves in a 2.5-layer model. J. Fluid Mech. 474, 85.
41. WINTERS, K. G. & D'ASARO, E. A. 1989 Two-dimensional instability of finite amplitude internal gravity wave packets near a critical level. J. Geophys, Res. 94, 12709.
42. YIH, C.-S. 1960 Exact solutions for steady two-dimensional flow of a stratified fluid. J. Fluid Mech. 9, 161.