A new analytical model for internal solitons in the ocean

Journal of Physical Oceanography

Volumn 33, Issue 11, 2003, Pages 2247-2269

  Apel, John R ^a   Jackson, Chris ^b  

^a Global Ocean Associates   (United States)

^b Global Ocean Associates   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DYNAMICS; FLOW OF FLUIDS; SOLITONS;

SOLITARY WAVES; STRATIFIED FLUID FLOW;

OCEANOGRAPHY;

ANALYTICAL METHOD; INTERNAL WAVE; NUMERICAL MODEL;

EID: 0442281593     PISSN: 00223670     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0485(2003)033<2247:ANAMFI>2.0.CO;2     Document Type: Article

References (78)

1. Alpers, W., and E. Salusti, 1983: Scylla and Charybdis observed from space. J. Geophys. Res., 88 (C3), 1800-1808.
2. Apel, J. R., 1999: Amplification of internal waves by shear-flow instability: A new view and new possibilities. Global Ocean Assciates Rep. GOA 99-2, 20 pp.
3. Apel, J. R., 2000: Solitons near Gibraltar: Views from the European Remote Sensing Satellites. Global Ocean Associates Rep. GOA 2000-1, 23 pp.
4. Apel, J. R., and F. I. Gonzalez, 1983: Nonlinear features of internal waves off Baja California as observed from the SEASAT Imaging Radar. J. Geophys. Res., 88 (C7), 4459-4466.
5. Apel, J. R., and J. R. Holbrook, 1983: Internal solitary waves in the Sulu Sea. Johns Hopkins APL Tech. Dig., 4, 267-275.
6. Apel, J. R., and J. R. Promi, H. M. Byrne, and R. L. Sellers, 1975a: Near-simultaneous observations of intermittent internal waves on the continental shelf from ship and aircraft. Geophys. Res. Lett., 2, 128-131.
7. Apel, J. R., and H. M. Byrne, J. R. Proni, and R. L. Charnell, 1975b: Observations of oceanic internal and surface waves from the Earth Resources Technology Satellite. J. Geophys. Res., 80, 865-881.
8. Apel, J. R., and J. R. Holbrook, J. Tsai, and A. K. Liu. 1985: The Sulu Sea internal soliton experiment. J. Phys. Oceanogr., 15, 1625-1651.
9. Apel, J. R., and R. F. Gasparovic, D. R. Thompson, and B. L. Gotwols, 1988: Signatures of surface wave/internal wave interactions: Experiment and theory. Dyn. Atmos. Oceans., 12, 89-106.
10. Apel, J.R., and Coauthors, 1997: An overview of the 1995 SWARM shallow-water internal wave acoustic scattering experiment. IEEE J. Oceanic Eng., 22, 465-500.
11. Apel, L.A Ostrovsky, and Y. A. Stepanyants, 1998: Internal solitons in the ocean. Global Ocean Associates Rep. GOA 98-3, 46 pp.
12. Armi, L., and D. M. Farmer, 1988: The flow of Mediterranean water through the Strait of Gibraltar. Progress in Oceanography, Vol. 21, Pergamon, 1-105.
13. Badiey, M., Y. Mu, J. Lynch, J. Apel. and S. Wolf, 2002: Temporal and azimuthal dependence of sound propagation in shallow water with internal waves. IEEE J. Oceanic Eng., 27, 117-129.
14. Benjamin, T. B., 1962: The solitary wave on a stream with an arbitrary distribution of vorticity, J. Fluid. Mech., 12, 97-116.
15. Benjamin, T.B., 1966: Internal waves of finite amplitude and permanent form. J. Fluid Mech., 25, 241-270.
16. Benney, D. J., 1966: Long non-linear waves in fluid flows. J. Math. Phys., 45, 52-63.
17. Booker, J. R., and F. B. Bretherton, 1967: The critical layer for internal gravity waves in a shear flow. J. Fluid. Mech., 27, 513-539.
18. Brandt, P., W. Alpers, and J. O. Backhaus, 1996: Study of the generation and propagation of internal waves in the Strait of Gibraltar using a numerical model and synthetic aperture radar images of the European ERS I satellite. J. Geophys. Res., 101, 14 237-14 252.
19. Dodd, R. K., J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, 1982: Solitons and Nonlinear Wave Equations. Academic Press, 630 pp.
20. Ekman, V. W., 1904: On dead water. Scientific Results of the Norwegian North Polar Expedition, 1893-96. Vol. 5, No. 15, 1-152.
21. Farmer, D. M., and J. D. Smith. 1978: Nonlinear waves in a fjord. Hydrodynamics of Estuaries and Fjords. J. C. H. Nihoul. Ed., Elsevier Scientific, 465-493.
22. Farmer, D. M., and J. D. Smith, 1980: Tidal interaction of stratified flow with a sill in Knight Inlet. Deep-Sea Res., 27A, 239-254.
23. Farmer, D. M., and L, Armi, 1988: The flow of Atlantic water through the Strait of Gibraltar. Progress in Oceanography. Vol. 21, Pergamon,1-105.
24. Farmer, D. M., and L. Armi, 1999a: The generation and trapping of solitary waves over topography. Science, 283, 188-190.
25. Farmer, D. M., and L. Armi, 1999b: Stratified flow over topography: The role of small-scale entrainment and mixing in flow establishment. Proc. Roy. Soc. London. 455A, 3221-3258.
26. Finette, S., M. H. Orr. A. Turgut. S. Wolf, B. Pasewark, and J. R. Apel, 1999, Acoustic field variability induced by time-evolving internal wave fields, J. Acoust. Soc. Amer., 108, 957-972.
27. Fu, L. L., and B. Holt, 1984: Internal waves in the Gulf of California: Observations from a spaceborne radar, J. Geophys. Res., 89 (C2). 2053-2060.
28. Gasparovic, R. F., and V. S. Etkin, 1994: An overview of the Joint US/Russia Internal Wave Remote Sensing Experiment. Proc. IGARSS '94, Pasadena, CA. IGARSS, 741-743.
29. Gasparovic, R. F., J. R. Apel, D. R. Thompson, and J. S. Toscho, 1986: A comparison of SIR-B synthetic aperture radar data with ocean internal wave measurements. Science, 232, 1529-1531.
30. Gasparovic, R. F., J. R. Apel, and E. S. Kasischke, 1988: An overview of the SAR internal wave signature experiment. J. Geophys. Res., 93 (C10). 12 304-12 316.
31. Gerkema, T., and J. T. F. Zimmerman, 1995: Generation of nonlinear internal tides and solitary waves. J. Phys. Oceanogr., 25, 1081-1094.
32. Grimshaw, R., 1981: Evolution equations for long nonlinear waves in stratified shear flows. Stud. Appl. Math., 65, 159-188.
33. Grimshaw, R., L. A. Ostrovsky, V. I. Shrira, and Yu. A. Stepanyants. 1998: Long nonlinear surface and internal gravity waves in a rotating ocean. Surveys Geophys., 19, 289-338.
34. Gurevich, A. V., and L. P.Pitaevskii, 1973a: Nonstationary structure of a collisionless shock wave (English translation). Sov. Phys. JETP. 38, 291-297.
35. Gurevich, A. V., and L. P.Pitaevskii, 1973b: Decay of initial discontinuity in the Korteweg-De Vries equation. JETP Lett. V. 17, 193-195.
36. Gurevich, A. V., A. L. Krylov, and G. A. El, 1990: Nonlinear modulated waves in dispersive hydrodynamics. Sov. Phys. JETP. 71, 899-910.
37. Haury, L. R., M. G. Briscoe, and M. H. Orr, 1979: Tidally generated internal wave packets in Massachusetts Bay. Nature, 278, 312-317.
38. Henyey, F. S., and A. Hoering, 1997: Energetics of borelike internal waves. J. Geophys. Res., 102, 3323-3330.
39. Holloway, P., E. Pelinovsky, and T. Talipova, 1999: A generalized Korteweg-de Vries model of internal tide transformation in the coastal zone. J. Geophys. Res., 104 (C8), 18 333-18 350.
40. Joseph, R. J., 1977: Solitary waves in a finite depth fluid. J. Phys. A: Math. Gen., 10 (12), L225-L227.
41. Kao, T. W., F.-S. Pan, and D. Renouard, 1985: Internal solitons on the pycnocline: Generation, propagation and shoating and breaking over a slope. J. Fluid Mech., 159, 19-53.
42. Keulegan, G. H., 1953: Characteristics of internal solitary waves. J. Res. Natl. Bur. Stand., 51, 133-140.
43. Keulegan, G. H., and L. H. Carpenter, 1961: An experimental study of internal progressive oscillatory waves. Natl. Bur. Stand. Rep. 7319, 34 pp.
44. Koop, C. C., and G. Butler, 1981: An investigation of internal solitary waves in a two-fluid system. J. Fluid Mech., 112, 225-251.
45. Korteweg, D. J., and G. de Vries, 1895: On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave. Phil. Mag., 39, 422-443.
46. Kropfli, R. A., L. A. Ostrovsky, T. P. Stanton, E. A. Skirta, A. N. Keane, and V. A. Irisov, 1999: Relationships between strong internal waves in the coastal zone and their radar and radiometric signatures. J. Geophys. Res., 104 (C2), 3133-3148.
47. Kubota, T., D. R. S. Ko, and L. Dobbs, 1978: Propagation of weakly nonlinear internal waves in a stratified fluid of finite depth. J. Hydronaut., 12, 157-165.
48. Lamb, H., 1932: Hydrodynamics. Cambridge University Press, 738 pp.
49. Lamb, K. G., 1994: Numerical experiments of internal wave generation by strong tidal flow across a finite amplitude bank edge. J. Geophys. Res., 99, 843-864.
50. Lee, C.-Y., and R. C. Beardsley, 1974: The generation of long non-linear internal waves in a weakly stratified shear flow. J. Geophys. Res., 79, 453-457.
51. Lindzen, R. S., 1988: Instability of plane parallel shear flow (toward a mechanistic picture of how it works). Pure Appl. Geophys., 126, 103-121.
52. Liu, A. K., 1988: Analysis of nonlinear internal waves in the New York Bight. J. Geophys. Res., 93 (C10), 12 317-12 329.
53. Liu, A. K., and J. Benney, 1981: The evolution of nonlinear wave trains in stratified shear flows. Stud. Appl. Math., 64, 247-269.
54. Liu, A. K., and J. R. Holbrook, and J. R. Apel, 1985: Nonlinear internal wave evolution in the Sulu Sea. J. Phys. Oceanogr., 15, 1613-1624.
55. Liu, A. K., S. Y. Chang, M.-K, Hsu, and N.K. Liang, 1998: Evolution of nonlinear internal waves in East and South China Seas. J. Geophys. Res., 103, 7995-8008.
56. Maslowe, S. A., and L. G. Redekopp, 1980: Long nonlinear waves in stratified shear flows. J. Fluid Mech., 101 (Part 2), 321-348.
57. Maxworthy, T., 1979: A note on the internal solitary waves produced by tidal flow over a three-dimensional ridge. J. Geophys. Res., 84, 338-346.
58. Miles, J. W., 1979: On internal solitary waves. Tellus, 31, 456-462.
59. Miles, J. W., 1980: Solitary waves.II Annu. Rev. Fluid Mech.12, 11-43.
60. Miles, J. W., 1981: On internal solitary waves. II. Tellus, 33, 397-401.
61. Orr, W. M. F., 1907: The stability or instability of the steady motions of a perfect liquid and a viscous liquid. Proc. Roy. Irish Acad., A27, 9-138.
62. Osborne, A. R., 1995: Solutions in the periodic Korteweg-de Vries equation, the -function representation, and the analysis of non-linear, stochastic wave trains. Phys. Rev. E. 52, 1105-1122.
63. Osborne, and T. L. Burch, 1980: Internal solitions in the Andaman Sea. Science, 208, 451-460.
64. Ostrovsky, L. A., 1978: Nonlinear internal waves in a rotating ocean. Oceanology, 18, 119-125.
65. Ostrovsky, L. A., and Y. A. Stepanyants, 1989: Do internal solitions exist in the ocean? Rev. Geophys., 27, 293-310.
66. Ostrovsky, L. A., and Y. S. Stepanyants, 1990: Nonlinear surface and internal waves in rotating fluids. Nonlinear Waves (in Russian), A.V. Gapon-Grekhov et al., Eds., Vol. 3, Springer-Verlag, 106-128.
67. Pinkel, R., M. Merrifield, M. McPhaden, J. Picaut, S. Rutledge, D: Siegel, and L. Washburn, 1997: Solitary waves in the western Equatorial Pacific Ocean. Geophys. Res. Lett., 24, 1603-1606.
68. Rocklift, N., 1984: Long nonlinear waves in stratified shear flows. Geophys. Astrophys. Fluid Dyn., 28, 55-75.
69. Russell, J. S., 1838: Report to committee on waves, Report of the 7th Meeting of British Association for the Advancement of Science, John Murray, 417-496.
70. Russell, J. S., 1844: Report on waves. Report of the 14th Meeting of British Association for the Advancement of Science, John Murray, 311-390.
71. Sandtröm, H., and J. A. Elliot, 1984: Internal tide and solitions on the Scotian Shelf: A nutrient pump at work. J. Geophys. Res. 89 (C4). 6415-6426.
72. Scott, A. C., F. Y. E. Chu, and D. W. McLaughlin, 1973: The solition: A new concept in applied science. Proc. IEEE, 61, 1443-1483.
73. Segur, H., and J. L. Hammack, 1982: Soliton models of long internal waves. J. Fluid Mech., 118, 285-304.
74. Stanton, T. P., and L. A. Ostrovsky, 1998: Observations of highly nonlinear internal solitons over the continental shelf. Geophys. Res. Lett., 25, 2695-2698.
75. Suvorov, A. M., 1981: Evolution of quasi-plane weakly nonlinear internal waves in a viscous fluid. Fluid Dyn., 16, 934-937.
76. Wesson, A.C., and M.C. Gregg. 1988: Turbulent dissipation in the Strait of Gibraltar and associated mixing. Small-Scale Turbulence and Mixing in the Ocean. J. C. J. Nihoul and B. M. Jamar, Eds., Elsevier, 201-212.
77. Zhang, R., and J. X, Zhou, 1997: Shallow Water Acoustics. China Ocean Press, 634 pp.
78. Zhou, J. X., X. Z. Zhang, and P. H. Rogers, 1991: Resonant interaction of a sound wave with internal solitons in the coastal zone. J. Acoust. Soc. Amer., 90, 2042-2054.