Oceanography The Official Magazine of
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Volume 25 Issue 02

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Volume 25, No. 2
Pages 108 - 123


The Generation of Nonlinear Internal Waves

By Christopher R. Jackson , José C.B. da Silva, and Gus Jeans 
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Article Abstract

Nonlinear internal waves are found in many parts of the world ocean. Their widespread distribution is a result of their origin in the barotropic tide and in the variety of ways they can be generated, including by lee waves, tidal beams, resonance, plumes, and the transformation of the internal tide. The differing generation mechanisms and diversity of generation locations and conditions all combine to produce waves that range in scale from a few tens of meters to kilometers, but with all properly described by solitary wave theory. The ability of oceanic nonlinear internal waves to persist for days after generation and the key role internal waves play in connecting large-scale tides to smaller-scale turbulence make them important for understanding the ocean environment.


Jackson, C.R., J.C.B. da Silva, and G. Jeans. 2012. The generation of nonlinear internal waves. Oceanography 25(2):108–123, https://doi.org/10.5670/oceanog.2012.46.


Akylas, T., and R. Grimshaw. 1992. Solitary internal waves with oscillatory tails. Journal of Fluid Mechanics 242:279–298, https://doi.org/10.1017/S0022112092002374.

Akylas, T.R., R.H.J. Grimshaw, S.R. Clark, and A. Tabaei. 2007. Reflecting tidal wave beams and local generation of solitary waves in the ocean thermocline. Journal of Fluid Mechanics 593:297–313, https://doi.org/10.1017/S0022112007008786.

Alford, M.H., J.B. Mickett, S. Zhang, P. MacCready, Z. Zhao, and J. Newton. 2012. Internal waves on the Washington continental shelf. Oceanography 25(2):66–79, https://doi.org/10.5670/oceanog.2012.43.

Alpers, W. 1985. Theory of radar imaging of internal waves. Nature 314:245–247, https://doi.org/10.1038/314245a0.

Apel, J.R., J.R. Holbrook, A.K. Liu, and J.J. Tsai. 1985. The Sulu Sea internal soliton experiment. Journal of Physical Oceanography 15(12):1,625–1,651, https://doi.org/10.1175/1520-0485(1985)015<1625:TSSISE>2.0.CO;2.

Armi, L., and D.M. Farmer. 1988. The flow of Mediterranean water through the Strait of Gibraltar. Progress in Oceanography 21:1–105, https://doi.org/10.1016/0079-6611(88)90055-9.

Azevedo, A., J.C.B. da Silva, and A.L. New. 2006. On the generation and propagation of internal solitary waves in the southern Bay of Biscay. Deep Sea Research Part I 53:927–941, https://doi.org/10.1016/j.dsr.2006.01.013.

Baines, P.G. 1982. On internal tide generation models. Deep Sea Research Part A 29:307–338, https://doi.org/10.1016/0198-0149(82)90098-X.

Bogucki, D., T. Dickey, and L.G. Redekopp. 1997. Sediment resuspension and mixing by resonantly generated internal solitary waves. Journal of Physical Oceanography 27:1,181–1,196, https://doi.org/10.1175/1520-0485(1997)027<1181:SRAMBR>2.0.CO;2.

Brickman, D., and J.W. Loder. 1993. Energetics of the internal tide on northern Georges Bank. Journal of Physical Oceanography 23:409–424.

Chao, S.-Y., P.-T. Shaw, M.-K. Hsu, and Y.J. Yang. 2006. Reflection and diffraction of internal solitary waves by a circular island. Journal of Oceanography 62:811–823, https://doi.org/10.1007/s10872-006-0100-4.

Chereskin, T.K. 1983. Generation of internal waves in Massachusetts Bay. Journal of Geophysical Research 88(C4):2,649–2,661, https://doi.org/10.1029/JC088iC04p02649.

Clarke, S.R., and R.H.J. Grimshaw. 1994. Resonantly generated internal waves in a contraction. Journal of Fluid Mechanics 274:139–161, https://doi.org/10.1017/S0022112094002077.

Cummins, P.F., S. Vagle, L. Armi, and D.M. Farmer. 2003. Stratified flow over topography: Upstream influence and generation of nonlinear internal waves. Proceedings of the Royal Society of London A 459:1,467–1,487, https://doi.org/10.1098/rspa.2002.1077.

da Silva, J.C.B., and K.R. Helfrich. 2008. Synthetic Aperture Radar observations of resonantly generated internal solitary waves at Race Point Channel (Cape Cod). Journal of Geophysical Research 113, C11016, https://doi.org/10.1029/2008JC005004.

da Silva, J.C.B., and J.M. Magalhães. 2009. Satellite observations of large atmospheric gravity waves in the Mozambique Channel. International Journal of Remote Sensing 30:1,161–1,182.

da Silva, J.C.B, A.L. New, and A. Azevedo. 2007. On the role of SAR for observing “local generation” of internal solitary waves off the Iberian Peninsula. Canadian Journal of Remote Sensing 33:388–403, https://doi.org/10.5589/m07-041.

da Silva, J.C.B., A.L. New, and J.M. Magalhães. 2009. Internal solitary waves in the Mozambique Channel: Observations and interpretation. Journal of Geophysical Research 114, C05001, https://doi.org/10.1029/2008JC005125.

da Silva, J.C.B., A.L. New, and J.M. Magalhães. 2011. On the structure and propagation of internal solitary waves generated at the Mascarene Plateau in the Indian Ocean. Deep-Sea Research Part I 58:229–240, https://doi.org/10.1016/j.dsr.2010.12.003.

Defant, A. 1960. Physical Oceanography, vol. II. Pergamon Press, Oxford, UK, 598 pp.

Farmer, D.M., M.H. Alford, R.-C. Lien, Y.J. Yang, M.-H. Chang, and Q. Li. 2011. Oceanography 24(4):64–77, https://doi.org/10.5670/oceanog.2011.95.

Farmer, D.M., and L. Armi. 1988. The flow of Atlantic water through the Strait of Gibraltar. Progress in Oceanography 21:1–105, https://doi.org/10.1016/0079-6611(88)90055-9.

Farmer, D.M., Q. Li, and J.-H. Park. 2009. Internal wave observations in the South China Sea: The role of rotation and nonlinearity. Atmosphere-Ocean 47:267–280, https://doi.org/10.3137/OC313.2009.

Farmer, D.M., and J.D. Smith. 1980. Tidal interaction of stratified flow with a sill in Knight Inlet. Deep Sea Research Part A 27:239–254, https://doi.org/10.1016/0198-0149(80)90015-1.

Gerkema, T. 1996. A unified model for the generation and fission of internal tides in a rotating ocean. Journal of Marine Research 54:421–450, https://doi.org/10.1357/0022240963213574.

Gerkema, T. 2001. Internal and interfacial tides: Beam scattering and local generation of solitary waves. Journal of Marine Research 59:227–255, https://doi.org/10.1357/002224001762882646.

Gerkema, T., and J.T.F. Zimmerman. 2008. An Introduction to Internal Waves. Lecture notes available online at: http://www.nioz.nl/public/fys/staff/leo_maas/courses/book.pdf (accessed May 26, 2012).

Grisouard, N., C. Staquet, and T. Gerkema. 2011. Generation of internal solitary waves in a pycnocline by an internal wave beam: A numerical study. Journal of Fluid Mechanics 676:491–513, https://doi.org/10.1017/jfm.2011.61.

Groeskamp, S., J.J. Nauw, and L.R.M. Maas. 2011. Observations of estuarine circulation and solitary internal waves in a highly energetic tidal channel. Ocean Dynamics 61:1,767–1,782, https://doi.org/10.1007/s10236-011-0455-y.

Halpern, D. 1971. Observations of short period internal waves in Massachusetts Bay. Journal of Marine Research 29:116–132.

Haury, L.R., M.G. Briscoe, and M.H. Orr. 1979. Tidally generated internal wave packets in Massachusetts Bay. Nature 278:313–317, https://doi.org/10.1038/278312a0.

Helfrich, K.R., and W.K. Melville. 1986. On long nonlinear internal waves over slope-shelf topography. Journal of Fluid Mechanics 167:285–308, https://doi.org/10.1017/S0022112086002823.

Helfrich, K.R., and W.K. Melville. 2006. Long nonlinear internal waves. Annual Review of Fluid Mechanics 38:395–425, https://doi.org/10.1146/annurev.fluid.38.050304.092129.

Henyey, F.S., and A. Hoering. 1997. Energetics of borelike internal waves. Journal of Geophysical Research 102(C2):3,323–3,330, https://doi.org/10.1029/96JC03558.

Holloway, P.E. 1987. Internal hydraulic jumps and solitons at a shelf break region on the Australian North West Shelf. Journal of Geophysical Research 92(C5):5,405–5,416, https://doi.org/10.1029/JC092iC05p05405.

Huthnance, J.M. 1981. Waves and currents near the continental shelf edge. Progress in Oceanography 10:193–226, https://doi.org/10.1016/0079-6611(81)90004-5.

Huthnance, J.M. 1995. Circulation, exchange and water masses at the ocean margin: The role of physical processes at the shelf edge. Progress in Oceanography 35:353–431, https://doi.org/10.1016/0079-6611(95)80003-C.

Hyder, P., D.R.G. Jeans, E. Cauquil, and R. Nerzic. 2005. Observations and predictability of internal solitons in the northern Andaman Sea. Applied Ocean Research 27:1–11, https://doi.org/10.1016/j.apor.2005.07.001.

Jackson, C.R. 2004. An Atlas of Internal Solitary-like Waves and Their Properties, 2nd ed. Global Ocean Associates, Alexandria, VA, 560 pp. Available at http://www.internalwaveatlas.com (accessed May 26, 2012).

Jackson, C.R. 2007. Internal wave detection using the Moderate Resolution Imaging Spectroradiometer (MODIS). Journal of Geophysical Research 112, C11012, https://doi.org/10.1029/2007JC004220.

Kilcher, L.F., and J.D. Nash. 2010. Structure and dynamics of the Columbia River tidal plume front. Journal of Geophysical Research 115, C05S90, https://doi.org/10.1029/2009JC006066.

Konyaev, K.V., K.D. Sabinin, and A.N. Serebryany. 1995. Large-amplitude internal waves at the Mascarene Ridge in the Indian Ocean. Deep Sea Research Part I 42:2,075–2,091, https://doi.org/10.1016/0967-0637(95)00067-4.

Kranenburg, C., J.D. Pietrzak, and G. Abraham. 1991. Trapped internal waves over undular topography. Journal of Fluid Mechanics 226:205–217, https://doi.org/10.1017/S0022112091002355.

La Violette, P.E., and R.A. Arnone. 1988. A tide-generated internal waveform in the western approaches to the Strait of Gibraltar. Journal of Geophysical Research 93(C12):15,653–15,667, https://doi.org/10.1029/JC093iC12p15653.

Magalhães, J.M., I.B. Araujo, J.C.B. da Silva, R.H.J. Grimshaw, K. Davis, and J. Pineda. 2011. Atmospheric gravity waves in the Red Sea: A new hotspot. Nonlinear Processes in Geophysics 18:71–79, https://doi.org/10.5194/npg-18-71-2011.

Matthews, J.P., H. Aiki, S. Masuda, T. Awaji, and Y. Ishikawa. 2011. Monsoon regulation of Lombok Strait internal waves. Journal of Geophysical Research 116, C05007, https://doi.org/10.1029/2010JC006403.

Maxworthy, T. 1979. A note on the internal solitary waves produced by tidal flow over a three-dimensional ridge. Journal of Geophysical Research 84(C1):338–346, https://doi.org/10.1029/JC084iC01p00338.

Melville, W.K., and K.R. Helfrich. 1987. Transcritical two-layer flow over topography. Journal of Fluid Mechanics 178:31– 52, https://doi.org/10.1017/S0022112087001101.

Melville, W.K., and E. Macomb. 1987. Transcritical flows in straits. Pp. 175–183 in Proceedings of the Third International Symposium on Stratified Flows, Pasadena, CA,February 3–5, 1987.

Mercier, M.J., M. Mathur, L. Gostiaux, T. Gerkema, J.M. Magalhães, J.C.B. da Silva, and T. Dauxois. In press. Soliton generation by internal tidal beams impinging on a pycnocline: Laboratory experiments. Journal of Fluid Mechanics.

Nash, J.D., and J.N. Moum. 2005. River plumes as a source of large-amplitude internal waves in the coastal ocean. Nature 437:400–403, https://doi.org/10.1038/nature03936.

New, A.L. 1988. Internal tidal mixing in the Bay of Biscay. Deep Sea Research Part A 5:691–709, https://doi.org/10.1016/0198-0149(88)90026-X.

New, A.L., and R.D. Pingree. 1992. Local generation of internal soliton packets in the central Bay of Biscay. Deep Sea Research Part A 9:1,521–1,534, https://doi.org/10.1016/0198-0149(92)90045-U.

New, A.L., and J.C.B. da Silva. 2002. Remote-sensing evidence for the local generation of internal soliton packets in the central Bay of Biscay. Deep Sea Research Part I 49:915–934, https://doi.org/10.1016/S0967-0637(01)00082-6.

Osborne, A.R., and T.L. Burch. 1980. Internal solitons in the Andaman Sea. Science 208:451–460, https://doi.org/10.1126/science.208.4443.451.

Ostrovsky, L.A., and Y.A. Stepanyants. 1989. Do internal solitons exist in the ocean? Reviews of Geophysics 27:293–310, https://doi.org/10.1029/RG027i003p00293.

Pietrzak, J.D., C. Kranenburg, and G. Abraham. 1990. Resonant internal waves in fluid flow. Nature 344:844–847, https://doi.org/10.1038/344844a0.

Pingree, R.D., D.K. Griffiths, and G.T. Mardell. 1983. The structure of the internal tide at the Celtic Sea shelf break. Journal of the Marine Biological Association of the United Kingdom 64:99–113, https://doi.org/10.1017/S002531540005966X.

Pingree, R.D., and G.T. Mardell. 1985. Solitary internal waves in the Celtic Sea. Progress in Oceanography 14:431–441, https://doi.org/10.1016/0079-6611(85)90021-7.

Pingree, R.D., G.T. Mardell, and A.L. New. 1986. Propagation of internal tides from the upper slopes of the Bay of Biscay. Nature 321:154–158, https://doi.org/10.1038/321154a0.

Pingree, R.D., and A.L. New. 1991. Abyssal penetration and bottom reflection of internal tidal energy in the Bay of Biscay. Journal of Physical Oceanography 21:28–39, https://doi.org/10.1175/1520-0485(1991)021<0028:APABRO>2.0.CO;2.

Redekopp, L.G., and Z. You. 1995. Passage through resonance for the forced Korteweg-de Vries equation. Physical Review Letters 74:5,158–5,161, https://doi.org/10.1103/PhysRevLett.74.5158.

Reeder, M.J., D.R. Christie, R.K. Smith, and R. Grimshaw. 1995. Interacting “Morning Glories” over northern Australia. Bulletin of the American Meteorological Society 76:1,165–1,171, https://doi.org/10.1175/1520-0477(1995)076<1165:IGONA>2.0.CO;2.

Russell, J.S. 1844. Report on waves. Pp. 311–390 in Report of the 14th Meeting of the British Association for the Advancement of Science. Jon Murray, London.

Sandstrom, H., and J.A. Elliott. 1984. Internal tide and solitons on the Scotian Shelf: A nutrient pump at work. Journal of Geophysical Research 89(C4):6,415–6,426, https://doi.org/10.1029/JC089iC04p06415.

Sandstrom, H., J.A. Elliott, and N.A. Cochrane. 1989. Observing groups of solitary internal waves and turbulence with BATFISH and echo-sounder. Journal of Physical Oceanography 19(7):987–997, https://doi.org/10.1175/1520-0485(1989)019<0987:OGOSIW>2.0.CO;2.

Scott, A.C. 2007. The Nonlinear Universe. Springer-Verlag, Berlin, Germany, 378 pp.

Sherwin, T.J., V.I. Vlasenko, N. Stashchuk, D.R.G. Jeans, and B. Jones. 2002. Along-slope generation as an explanation for some unusually large internal tides. Deep-Sea Research Part I 49:1,787–1,799, https://doi.org/10.1016/S0967-0637(02)00096-1.

Shroyer, E. 2008. Science box: Varicose waves. Oceanography 21(4):28

Shroyer, E., J.N. Moum, and J.D. Nash. 2010. Mode 2 waves on the continental shelf: Ephemeral components of the nonlinear internal wavefield. Journal of Geophysical Research 115, C07001, https://doi.org/10.1029/2009JC005605.

Simmons, H., M.-H. Chang, Y.-T. Chang, S.-Y. Chao, O. Fringer, C.R. Jackson, and D.S. Ko. 2011. Modeling and prediction of internal waves in the South China Sea. Oceanography 24(4):88–99, https://doi.org/10.5670/oceanog.2011.97.

Smith, R.K., N. Crook, and G. Roff. 1982. The Morning Glory: An extraordinary atmospheric undular bore. Quarterly Journal of the Royal Meteorological Society 108:937–956, https://doi.org/10.1002/qj.49710845813.

Smyth, N.F., and P.E. Holloway. 1988. Hydraulic jump and undular bore formation on a shelf break. Journal of Physical Oceanography 18(7):947–962, https://doi.org/10.1175/1520-0485(1988)018<0947:HJAUBF>2.0.CO;2.

Stastna, M. 2011. Resonant generation of internal waves by short length scale topography. Physics of Fluids 23, 116601, https://doi.org/10.1063/1.3658773.

Stastna, M., and W.R. Peltier. 2005. On the resonant generation of large-amplitude internal solitary and solitary-like waves. Journal of Fluid Mechanics 543:267–292, https://doi.org/10.1017/S002211200500652X.

Vlasenko, V.I., and K. Hutter. 2001. Generation of second mode solitary waves by the interaction of a first mode soliton with a sill. Nonlinear Processes in Geophysics 8:223–239, https://doi.org/10.5194/npg-8-223-2001.

Vlasenko, V., N. Stashchuk, C. Guo, and X. Chen. 2010. Multimodal structure of baroclinic tides in the South China Sea. Nonlinear Processes in Geophysics 17:529–543, https://doi.org/10.5194/npg-17-529-2010.

Yang, Y.J., Y.C. Fang, M.-H. Chang, S.R. Ramp, C.-C. Kao, and T.Y. Tang. 2009. Observations of second baroclinic mode internal solitary waves on the continental slope of the northern South China Sea. Journal of Geophysical Research 114, C10003, https://doi.org/10.1029/2009JC005318.

Zabusky, N.J., and M.D. Kruskal. 1965. Interaction of “solitons” in a collisionless plasma and the recurrence of initial states. Physical Review Letters 15:240–243, https://doi.org/10.1103/PhysRevLett.15.240.

Zabusky, N.J., and M.A. Porter. 2010. Soliton. Scholarpedia 5(8):2,068, http://www.scholarpedia.org/article/Soliton.

Zhou, J.-X., and X.-Z. Zhang. 1991. Resonant interaction of sound wave with internal solitons in the coastal zone. Journal of the Acoustical Society of America 90(4):2,042–2,054, https://doi.org/10.1121/1.401632.

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