Internal solitons in laboratory experiments: Comparison with theoretical models

Chaos

Volumn 15, Issue 3, 2005, Pages

  Ostrovsky, L A ^a,b   Stepanyants, Y A ^b,c  

^a NOAA EARTH SYSTEM RESEARCH LABORATORY   (United States)

^b INSTITUTE OF APPLIED PHYSICS   (Russian Federation)

^c AUSTRALIAN NUCLEAR SCIENCE AND TECHNOLOGY ORGANISATION   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31144449936     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2107087     Document Type: Article

References (108)

1. B. Franklin, " Behavior of oil on water. Letter to John Pringle. Philadelphia, Dec. 1, 1762., " in Experiments and Observations on Electricity, London, 1769, pp. 142-144.
2. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM, Philadelphia, 1981).
3. L. A. Ostrovsky, " Nonlinear internal waves in the ocean., " in Nonlinear Waves, Proceedings of IV Gorky School on Nonlinear Waves, 1979, pp. 292-329 (in Russian).
4. R. Grimshaw, " Internal solitary waves., " Chap. in the book Environmental Stratified Flows, edited by, R. Grimshaw, (Kluwer Academic, New York, 2002), pp. 1-27.
5. L. A. Ostrovsky, " Nonlinear internal waves in a rotating ocean., " Okeanologia 18, 181-191 (1978) (in Russian) L. A. Ostrovsky, [English translation: Oceanology (Engl. Transl.) 18, 119-125 (1978)].
6. L. A. Ostrovsky, " Nonlinear internal waves in a rotating ocean., " Okeanologia 18, 181-191 (1978) (in Russian) L. A. Ostrovsky, [English translation: Oceanology (Engl. Transl.) 18, 119-125 (1978)].
7. L. A. Ostrovsky and Yu. A. Stepanyants, " Do internal solitons exist in the ocean?, " Rev. Geophys. 27, 293-310 (1989).
8. J. R. Apel, L. A. Ostrovsky, Y. A. Stepanyants, and J. F. Lynch, " Internal solitons in the ocean., " Technical Report WHOI-05, 2005. See also http://www.whoi.edu/science/
9. J. R. Apel, L. A. Ostrovsky, Y. A. Stepanyants, and J. F. Lynch, " Internal solitons in the ocean., " Technical Report WHOI-05, 2005. See also http://www.whoi.edu/science/
10. L. R. Walker, " Interfacial solitary waves in a two-fluid medium., " Phys. Fluids 16, 1796-1804 (1973).
11. T. Kakutani and N. Yamasaki, " Solitary waves on a two-layer fluid., " J. Phys. Soc. Jpn. 45, 674-679 (1978).
12. C. Leone, H. Segur, and J. L. Hammack, " Viscous decay of long internal solitary waves., " Phys. Fluids 25, 942-244 (1982).
13. G. H. Keulegan, " Characteristics of internal solitary waves., " J. Res. Natl. Bur. Stand. 51, 133-140 (1953).
14. R. Grimshaw, E. N. Pelinovsky, and T. G. Talipova, " The modified Korteweg-de Vries equation in the theory of large-amplitude internal waves., " Nonlinear Processes Geophys. 4, 237-250 (1997).
15. T. G. Talipova, E. N. Pelinovsky, K. Lamb, R. Grimshaw, and P. Holloway, " Cubic nonlinearity effects in the propagation of intense internal waves., " Dokl. Akad. Nauk SSSR 364, 824-827 (1999) (in Russian) T. G. Talipova, E. N. Pelinovsky, K. Lamb, R. Grimshaw, and P. Holloway, [English translation: Dokl. Earth Sci. 365, 241-244 (1999)].
16. T. G. Talipova, E. N. Pelinovsky, K. Lamb, R. Grimshaw, and P. Holloway, " Cubic nonlinearity effects in the propagation of intense internal waves., " Dokl. Akad. Nauk SSSR 364, 824-827 (1999) (in Russian) T. G. Talipova, E. N. Pelinovsky, K. Lamb, R. Grimshaw, and P. Holloway, [English translation: Dokl. Earth Sci. 365, 241-244 (1999)].
17. M. Funacoshi and M. Oikawa, " Long internal waves of large amplitude in a two-layer fluid., " J. Phys. Soc. Jpn. 55, 128-144 (1986).
18. R. Grimshaw, E. Pelinovsky, Y. Stepanyants, and T. Talipova, " Modeling internal solitary waves on the Australian North West Shelf., " Mar. Freshwater Res. (to be published). See also preprint 05-05, Loughborough University, Department of Mathematical Sciences, 15 pages; website: http://www.lboro.ac.uk/departments/ma/preprints/papers05/05-05abs.html
19. R. E. Davis and A. Acrivos, " Solitary internal waves in deep water., " J. Fluid Mech. 29, 593-607 (1967).
20. T. W. Kao and H. P. Pao, " Wake collapse in the thermocline and internal solitary waves., " J. Fluid Mech. 97, 115-127 (1979).
21. T. W. Kao, F.-Sh. Pan, and D. Renouard, " Internal solitons on the pycnocline: Generation, propagation, and shoaling and breaking over a slope., " J. Fluid Mech. 159, 19-53 (1985).
22. J. Gan and R. G. Ingram, " Internal hydraulics, solitons and associated mixing in a stratified Sound., " J. Geophys. Res. 97, 9669-9688 (1992).
23. V. I. Karpman, Nonlinear Waves in Dispersive Media (Nauka, Moscow, 1973) (in Russian) [English translation: Nonlinear Waves in Dispersive Media (Pergamon, Oxford, 1973)].
24. V. I. Karpman, Nonlinear Waves in Dispersive Media (Nauka, Moscow, 1973) (in Russian) [English translation: Nonlinear Waves in Dispersive Media (Pergamon, Oxford, 1973)].
25. C. Koop and G. Butler, " An investigation of internal solitary waves in a two-fluid system., " J. Fluid Mech. 112, 225-251 (1981).
26. H. Segur and J. L. Hammack, " Soliton models of long internal waves., " J. Fluid Mech. 118, 285-304 (1982).
27. V. I. Bukreev and N. V. Gavrilov, " Experimental investigation of solitary internal waves in a two-layer fluid., " Zh. Prikl. Mekh. Tekhn. Fiziki (PMTF) N.5, 51-56 (1983) (in Russian) V. I. Bukreev and N. V. Gavrilov, [English translation: Sov. Phys. J. Appl. Mech. Tech. Phys. n.5 (1983)].
28. V. I. Bukreev and N. V. Gavrilov, " Experimental investigation of solitary internal waves in a two-layer fluid., " Zh. Prikl. Mekh. Tekhn. Fiziki (PMTF) N.5, 51-56 (1983) (in Russian) V. I. Bukreev and N. V. Gavrilov, [English translation: Sov. Phys. J. Appl. Mech. Tech. Phys. n.5 (1983)].
29. K. A. Gorshkov and V. V. Papko, " Non-adiabatic stage of damping of solitons and the intermediate asymptotics., " Izv. Vyssh. Uchebn. Zaved., Radiofiz. 20, 360-365 (1977) (in Russian)
30. [English translation: Radiophys. Quantum Electron. 20, (1977)].
31. Ch.-Y. Lee and R. C. Beardsley, " The generation of long nonlinear internal waves in a weakly stratified shear flows., " J. Geophys. Res. 79, 453-457 (1974).
32. J. Gear and R. Grimshaw, " A second-order theory for solitary waves in shallow fluids., " Phys. Fluids 26, 14-29 (1983).
33. A. K. Liu, J. R. Holbrook, and J. R. Apel, " Nonlinear internal wave evolution in the Sulu Sea., " J. Phys. Oceanogr. 15, 1613-1624 (1985).
34. L. Ostrovsky and E. Pelinovsky, " Nonlinear evolution of tsunami waves., " Bull. Roy. Soc. New Zealand 15, 203-211 (1976).
35. A. R. Osborne, " The inverse scattering transform: tools for the nonlinear Fourier analysis and filtering of ocean surface waves., " Chaos, Solitons Fractals 5, 2623-2637 (1995).
36. J.-G. Caputo and Y. A. Stepanyants, " Bore Formation, Evolution and Disintegration into Solitons in Shallow Inhomogeneous Channels., " Nonlinear Processes Geophys. 10, 407-424 (2003).
37. R. Grimshaw, " The solitary wave in water of variable depth., " J. Fluid Mech. 0022-1120 42, 639-656 (1970); R. Grimshaw, " The solitary wave in water of variable depth. Part 2., " J. Fluid Mech. 46, 611-622 (1971).
38. R. Grimshaw, " The solitary wave in water of variable depth., " J. Fluid Mech. 0022-1120 42, 639-656 (1970); R. Grimshaw, " The solitary wave in water of variable depth. Part 2., " J. Fluid Mech. 46, 611-622 (1971).
39. T. Kakutani and K. Matsuuchi, " Effect of viscosity on long gravity waves., " J. Phys. Soc. Jpn. 39, 237-246 (1975).
40. J. W. Miles, " Damping of weakly nonlinear shallow-water waves., " J. Fluid Mech. 76, 251-257 (1976).
41. K. P. Das and J. Chakrabarti, " The Korteweg-de Vries equation modified by viscosity for waves in a two-layer fluid in a channel of arbitrary cross section., " Phys. Fluids 29, 661-666 (1986).
42. K. R. Helfrich, " Internal solitary wave breaking and run-up on a uniform slope., " J. Fluid Mech. 243, 133-154 (1992).
43. K. A. Gorshkov and L. A. Ostrovsky, " Interaction of solitons in non-integrable systems: Direct perturbation method and applications., " Physica D 3, 248-438 (1981).
44. R. Grimshaw, " Evolution equations for weakly nonlinear long internal waves in a rotating fluid., " Stud. Appl. Math. 73, 1-33 (1985).
45. D. Renouard and J.-P. Germain, " Experimental study of long nonlinear internal waves in rotating fluid., " Ann. Geophys. (Germany) 12, 254-264 (1994).
46. L. A. Ostrovsky and Yu. A. Stepanyants, " Nonlinear surface and internal waves in rotating fluids., " in Nonlinear Waves 3, Proceedings of the 1989 Gorky School on Nonlinear Waves, edited by, A. V. Gaponov-Grekhov, M. I. Rabinovich, and, J. Engelbrecht, (Springer-Verlag, Berlin, Heidelberg, 1990), pp. 106-128. [In Russian: in Nonlinear Waves. Physics and Astrophysics (Nauka, Moscow, 1993), pp. 132-153.]
47. L. A. Ostrovsky and Yu. A. Stepanyants, " Nonlinear surface and internal waves in rotating fluids., " in Nonlinear Waves 3, Proceedings of the 1989 Gorky School on Nonlinear Waves, edited by, A. V. Gaponov-Grekhov, M. I. Rabinovich, and, J. Engelbrecht, (Springer-Verlag, Berlin, Heidelberg, 1990), pp. 106-128. [In Russian: in Nonlinear Waves. Physics and Astrophysics (Nauka, Moscow, 1993), pp. 132-153.]
48. R. H. J. Grimshaw, L. A. Ostrovsky, V. I. Shrira, and Y. A. Stepanyants, " Long nonlinear surface and internal gravity waves in a rotating ocean., " Surv. Geophys. 19, 289-338 (1998).
49. A. L. New and M. Esteban, " A new Korteweg-de Vries-type theory for internal solitary waves in a rotating continuously-stratified ocean., " in Near-Surface Ocean Layer. V. 1. Physical Processes and Remote Sensing, Collection of Scientific Papers, edited by, E. N. Pelinovsky, and, V. I. Talanov, Nizhny Novgorod, IAP RAS, 1999, pp. 173-203.
50. Y. Liu and V. Varlamov, " Stability of solitary waves and weak rotation limit for the Ostrovsky equation., " J. Diff. Eqns. 203, 159-183 (2004).
51. R. H. J. Grimshaw, J.-M. He, and L. A. Ostrovsky, " Terminal damping of a solitary wave due to radiation in rotational systems., " Stud. Appl. Math. 101, 197-210 (1998).
52. O. A. Gilman, R. Grimshaw, and Yu. A. Stepanyants, " Dynamics of internal solitary waves in a rotating fluid., " Dyn. Atmos. Oceans 23, 403-411 (1996) (special issue. Stratified flows, Pt. A).
53. V. O. Vakhnenko, " High-frequency soliton-like waves in a relaxing medium., " J. Math. Phys. 40, 2011-2020 (1999).
54. Y. Stepanyants, " On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons., " Chaos, Solitons Fractals 28, 193-204 (2006).
55. A. I. Leonov, " The effect of Earth rotation on the propagation of weak nonlinear surface and internal long oceanic waves., " Ann. N.Y. Acad. Sci. 373, 150-159 (1981).
56. V. M. Galkin and Yu. A. Stepanyants, " On the existence of stationary solitary waves in a rotating fluid., " Prikl. Mat. Mekh. 0032-8235 55, 1051-1055 (1991) (in Russian) V. M. Galkin and Yu. A. Stepanyants, [English translation: J. Appl. Math. Mech. 55, 939-943 (1991)].
57. V. M. Galkin and Yu. A. Stepanyants, " On the existence of stationary solitary waves in a rotating fluid., " Prikl. Mat. Mekh. 0032-8235 55, 1051-1055 (1991) (in Russian) V. M. Galkin and Yu. A. Stepanyants, [English translation: J. Appl. Math. Mech. 55, 939-943 (1991)].
58. M. A. Obregon and Yu. A. Stepanyants, " Oblique magneto-acoustic solitons in a rotating plasma., " Phys. Lett. A 249, 315-323 (1998).
59. O. A. Gilman, R. Grimshaw, and Yu. A. Stepanyants, " Approximate analytical and numerical solutions of the stationary Ostrovsky equation., " Stud. Appl. Math. 95, 115-126 (1995).
60. T. Gerkema, " A unified model for the generation and fission of internal tides in a rotating ocean., " J. Mar. Res. 54, 421-450 (1996).
61. R. Plougonven and V. Zeitlin, " On periodic inertia-gravity waves of finite amplitude propagating without change of form at sharp density-gradient interfaces in the rotating fluid., " Phys. Lett. A 314, 140-149 (2003).
62. Yu. A. Stepanyants, " Experimental investigation of cylindrically diverging solitons in an electric lattice., " Wave Motion 3, 335-341 (1981).
63. A. A. Dorfman, E. N. Pelinovsky, and Yu. A. Stepanyants, " Finite-amplitude cylindrical and spherical waves in weakly dispersive media., " Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki (PMTF) N.2, 78-85 (1981) (in Russian) A. A. Dorfman, E. N. Pelinovsky, and Yu. A. Stepanyants [English translation: Sov. Phys. J. Appl. Mech. Tech. Phys. n.2, 206-211 (1982)].
64. A. A. Dorfman, E. N. Pelinovsky, and Yu. A. Stepanyants, " Finite-amplitude cylindrical and spherical waves in weakly dispersive media., " Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki (PMTF) N.2, 78-85 (1981) (in Russian) A. A. Dorfman, E. N. Pelinovsky, and Yu. A. Stepanyants [English translation: Sov. Phys. J. Appl. Mech. Tech. Phys. n.2, 206-211 (1982)].
65. C. Ramirez, D. Renouard, and Yu. A. Stepanyants, " Propagation of cylindrical waves in a rotating fluid., " Fluid Dyn. Res. 30, 169-196 (2002).
66. S. V. Iordansky, " Asymptotic behaviour of an axially symmetric diverging wave in a heavy liquid., " Dokl. Akad. Nauk SSSR 0002-3264 125, 1211-1214 (in Russian) (1959) S. V. Iordansky, [English translation: Sov. Phys. Dokl. 125, 6-9 (1959)].
67. S. V. Iordansky, " Asymptotic behaviour of an axially symmetric diverging wave in a heavy liquid., " Dokl. Akad. Nauk SSSR 0002-3264 125, 1211-1214 (in Russian) (1959) S. V. Iordansky, [English translation: Sov. Phys. Dokl. 125, 6-9 (1959)].
68. S. Maxon and J. Viecelli, " Cylindrical solitons., " Phys. Fluids 17, 1614-1616 (1974).
69. F. Calogero and A. Degasperis, " Solution by the spectral-transform method of a nonlinear evolution equation including as a special case the cylindrical KdV equation., " Lett. Nuovo Cimento 23, 150-154 (1978).
70. A. Nakamura and H. H. Chen, " Soliton solutions of the cylindrical KdV equation., " J. Phys. Soc. Jpn. 50, 711-718 (1981).
71. C. J. Amick and R. E. L. Turner, " A global theory of internal solitary waves in two-fluid system., " Trans. Am. Math. Soc. 298, 431-484 (1986).
72. R. E. L. Turner and J.-M. Vanden-Broeck, " Broadening of interfacial solitary waves., " Phys. Fluids 31, 2486-2490 (1988).
73. W. A. B. Evans and M. J. Ford, " An integral equation approach to internal (2-layer) solitary waves., " Phys. Fluids 8, 2032-2047 (1996).
74. J. Grue, A. Jensen, P.-O. Rusås, and J. K. Sveen, " Properties of large amplitude internal waves., " J. Fluid Mech. 380, 257-278 (1999).
75. V. I. Vlasenko and K. Hutter, " Numerical experiments on the breaking of solitary internal waves over a slope-shelf topography., " J. Phys. Oceanogr. 32, 1779-1793 (2002).
76. V. I. Vlasenko and K. Hutter, " Transformation and disintegration of strongly nonlinear internal waves by topography in stratified lakes., " Ann. Geophys. (Germany) 20, 2087-2013 (2002).
77. K. G. Lamb, " A numerical investigation of solitary internal waves with trapped cores formed via shoaling., " J. Fluid Mech. 451, 109-144 (2002).
78. K. G. Lamb, " Shoaling solitary internal waves: on a criterion for the formation of waves with trapped cores., " J. Fluid Mech. 478, 81-100 (2003).
79. M. Stastna and K. G. Lamb, " Large fully nonlinear internal solitary waves: The effect of background current., " Phys. Fluids 14, 2987-2999 (2002).
80. G. B. Whitham, " Variational methods and applications to water waves., " Proc. R. Soc. London, Ser. A 299, 6-25 (1967).
81. M. Miyata, " An internal solitary wave of large amplitude., " La Mer 23, 43-48 (1985).
82. M. Miyata, " Long internal waves of large amplitude., " in Nonlinear Water Waves, edited by, K. Horikawa, and, H. Maruo, (Springer-Verlag, Berlin, 1988), pp. 399-406.
83. M. Miyata, " A note on broad narrow solitary waves., " IPRC Report 00-01, SOEST, University of Hawaii, Honolulu, 00-05, 2000, p. 47.
84. H. Michallet and E. Barth́lemy, " Experimental study of interfacial solitary waves., " J. Fluid Mech. 366, 159-177 (1998).
85. W. Choi and R. Camassa, " Fully nonlinear internal waves in a two-fluid system., " J. Fluid Mech. 386, 1-36 (1999).
86. L. A. Ostrovsky and J. Grue, " Evolution equations for strongly nonlinear internal waves., " Phys. Fluids 15, 2934-2948 (2003).
87. L. A. Ostrovsky, in The 1998 WHOI/IOS/ONR Internal Solitary Wave Workshop: Contributed Papers, edited by, T. F. Duda, and, D. M. Farmer, Technical Report, WHOI 99-07, 1999, pp. 224-229.
88. A. V. Slunyaev, E. N. Pelinovsky, O. E. Poloukhina, and S. L. Gavrilyuk, " The Gardner equation as the model for long internal waves., " in Topical Problems of Nonlinear Wave Physics, Proceedings of the International Symposium, Inst. of Appl. Phys., RAS, Nizhny Novgorod, 2003, pp. 368-369.
89. S. M. Khasanov, " The propagation of Kelvin's solitary waves in an absorbing medium., " Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 0002-3515 25, 307-311, 1989 (in Russian) S. M. Khasanov, [English translation: Izv., Acad. Sci., USSR, Atmos. Oceanic Phys. 25, 3-6 (1989)].
90. S. M. Khasanov, " The propagation of Kelvin's solitary waves in an absorbing medium., " Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 0002-3515 25, 307-311, 1989 (in Russian) S. M. Khasanov, [English translation: Izv., Acad. Sci., USSR, Atmos. Oceanic Phys. 25, 3-6 (1989)].
91. G. H. Keulegan, " Gradual damping of solitary waves., " J. Res. Natl. Bur. Stand. 40, 480-487 (1948).
92. N. V. Gavrilov, " Internal solitary waves of large amplitude in a two-layer fluid., " Zh. Prikl. Mekh. i Tekhn. Fiziki (PMTF) N.5, 49-54 (1986) (in Russian) N. V. Gavrilov, [English translation: Sov. Phys. J. Appl. Mech. Tech. Phys. n.5 (1986)].
93. N. V. Gavrilov, " Internal solitary waves of large amplitude in a two-layer fluid., " Zh. Prikl. Mekh. i Tekhn. Fiziki (PMTF) N.5, 49-54 (1986) (in Russian) N. V. Gavrilov, [English translation: Sov. Phys. J. Appl. Mech. Tech. Phys. n.5 (1986)].
94. L. V. Ovsyannikov, et al., Nonlinear Problems of the Theory of Surface and Internal Waves (Nauka, Novosibirsk, 1985), in Russian.
95. V. V. Papko (private communication).
96. T. Gerkema and J. T. F. Zimmerman, " Generation of nonlinear internal tides and solitary waves., " J. Phys. Oceanogr. 25, 1081-1094 (1995).
97. A. P. Stamp and M. Jacka, " Deep-water internal solitary waves., " J. Fluid Mech. 305, 347-371 (1995).
98. D. I. Pullin and R. H. J. Grimshaw, " Large-amplitude solitary waves at the interface between two homogeneous fluids., " Phys. Fluids 31, 3550-3559 (1988).
99. K. K. Tung, T. F. Chan, and T. Kubota, " Large amplitude internal wave of permanent form., " Stud. Appl. Math. 66, 1-44 (1982).
100. B. Turkington, A. Eydeland, and S. Wang, " A computational model for solitary internal waves in a continuously stratified fluid., " Stud. Appl. Math. 85, 93-104 (1991).
101. J. Grue, A. Jensen, P.-O. Rusås, and J. K. Sveen, " Breaking and broadening of internal solitary waves., " J. Fluid Mech. 413, 181-217 (2000).
102. W. K. Melville and K. R. Helfrich, " Transcritical two-layer flow over topography., " J. Fluid Mech. 178, 31-52 (1987).
103. J. Grue, A. Fris, E. Palm, and P. O. Rusås, " A method for computing unsteady fully nonlinear interfacial waves., " J. Fluid Mech. 351, 223-252 (1997).
104. T. Maxworthy, " A note on the internal solitary waves produced by tidal flow over a three-dimensional ridge., " J. Geophys. Res. 84, 338-346 (1979).
105. J. K. Sveen, Y. Guo, P. Davies, and J. Grue, " On the breaking of internal waves at a ridge., " J. Fluid Mech. 469, 161-188 (2002).
106. J. Grue, " Generation, propagation and breaking of internal solitons., " Chaos this issue.
107. R. Grimshaw " Adjustment processes and radiating solitary waves in a regularised Ostrovsky equation., " Eur. J. Mech. B/Fluids 18, 535-543 (1999).
108. E. J. Parkes, " Explicit solutions of the reduced Ostrovsky equation. " (in press).