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5 - Waves – wave theory and wave dynamics

from Part II - Coastal Processes



Wave theories provide a mathematical description of changes in the form of waves, and the orbital motion associated with them, from deep water to the breaker line and into the surf zone. Because of the limitations imposed by assumptions about the wave form and water depth, no one theory is valid over the full range of conditions. The theories can be used simply to predict wave height, celerity and length in any water depth as well as functions associated with the orbital motion, such as the maximum orbital motion near the bed and the orbital diameter. The formulae for the simplest theories can be programmed in a spread sheet, and there are computer programs available that will provide solutions for all of the basic theories. These theories also provide the basis for complex numerical simulation models that are used to predict waves, currents and sediment transport in the nearshore and breaker zones.

Wave shoaling describes changes to the wave form and orbital motion as it moves into shallow water. During the process of shoaling, interaction with the underwater topography results in a bending of the direction of travel of the wave crests so that they conform to the shape of the depth contours, a process termed wave refraction. Wave refraction leads to a concentration of wave energy in some location, especially headlands, and a divergence of energy in other areas.

Further reading
Basco, D. R., 1985. A qualitative description of wave breaking. Journal of Waterway, Port, Coastal and Ocean Engineering, 111, 171–188.
Airy, G. B. 1845. Tides and waves. Encyclopaedia Metropolitan, pp. 241–396.
Baldock, T. E., Huntley, D. A, Bird, P. A. D., O'Hare, T. O. and Bullock, G. N. 1999. Breakpoint generated surf beat induced by bichromatic wave groups. Coastal Engineering, 39, 213–242.
Baldock, T. E., Holmes, P. and Horn, D. P. 1997. Low frequency swash motion induced by wave grouping. Coastal Engineering, 32, 197–222.
Basco, D. R., 1985. A qualitative description of wave breaking. Journal of Waterway, Port, Coastal and Ocean Engineering, 111, 171–188.
Battjes, J. A. 1974. Surf similarity. Proceedings of the 14th Coastal Engineering Conference, ASCE, pp. 466–480.
Bauer, B. O. 1990. Assessing the relative energetics of infragravity motions in lakes and seas. Journal of Coastal Research, 6, 853–865.
Bauer, B. O. and Greenwood, B, 1988. Surf zone similarity. Geographical Review, 78, 137–147.
Bayram, A. and Larson, M. 2000. Wave transformation in the nearshore zone: comparison between a Boussinesq model and field data. Coastal Engineering, 39, 149–171.
Bowen, A. J. 1969. Rip currents.1. Theoretical investigations. Journal of Geophysical Research, 74, 5467–5478.
Bowen, A. J., Inman, D. L. and Simmons, V. P. 1968. Wave set down and set up. Journal of Geophysical Research, 73, 2569–2577.
Bryant, E. A. 2001. Tsunami–The Underrated Hazard. Cambridge University Press, Melbourne, 350 pp.
Byrne, R. J. 1969. Field occurrences of induced multiple gravity waves. Journal of Geophysical Research, 74, 2590–2596.
Carrier, G. F. and Greenspan, H. P. 1958. Water waves of finite amplitude on a sloping beach. Journal of Fluid Mechanics, 4, 97–109.
Chester, D. K. 2001. The 1755 Lisbon Earthquake. Progress in Physical Geography, 25, 363–383.
Clague, J. J., Bobrowsky, P. T. and Hutchinson, I. 2000. A review of geological records of large tsunamis at Vancouver Island, British Columbia, and implications for hazard. Quaternary Science Reviews, 19, 849–863.
Choowong, M., Murakoshi, N., Hisada, K., and six others. 2008. 2004 Indian Ocean tsunami inflow and outflow at Phuket, Thailand. Marine Geology, 248, 179–192.
Coleman, P. J. 1968. Tsunamis as geological agents. Journal of the Geological Society of Australia, 15, 267–273.
Dally, W. R., Dean, R. G. and Dalrymple, R. A. 1985. Wave height variation across beaches of arbitrary profile. Journal of Geophysical Research, 90, 11917–11927.
Davidson-Arnott, R. G. D. and Randall, D. C. 1984. Spatial and temporal variations in spectra of storm waves across a barred nearshore. Marine Geology, 60, 15–30.
Davidson-Arnott, R. G. D. and Amin, S. M. N. 1985. An Approach to the problem of coastal erosion in Quaternary sediments. Applied Geography, 5, 99–110.
Davies, J. L. 1958. Wave refraction and the evolution of shoreline curves. Geographical Studies, 5, 1–14.
Dawson, J. C., Davidson-Arnott, R. G. D. and Ollerhead, J. 2002. Low-energy morphodynamics of a ridge and runnel system. Journal of Coastal Research, SI 36, 198–215.
Dawson, A. G. and Stewart, I. 2007. Tsunami deposits in the geological record. Sedimentary Geology, 200, 166–183.
Dean, R. G. 1965. Stream function representation of non-linear ocean waves. Journal of. Geophysical Research, 70, 4561–4572.
Demirbilek, Z. and Vincent, C. L. 2002. Water Wave Mechanics. Chapter 1 in EM 1110–2–1100 Part 2, Coastal Engineering Manual, US Army Corps of Engineers, 121 pp.
Dobson, R. S. 1967. Some Applications of a Digital Computer to Hydraulic Engineering Problems. Stanford University Department of Civil Engineering. Technical Report 80, 7–35.
Douglas, S. L. 1990. Influence of wind on breaking waves. Journal of Waterway, Port, Coastal and Ocean Engineering, 116, 651–663.
Duncan, J. H. 1981. An experimental investigation of breaking waves produced by a towed hydrofoil. Proceedings of the Royal Society of London A,377, 331–348.
Duncan, J. H. 2001. Spilling Breakers. Annual Review of Fluid Mechanics, 33, 519–547.
Elgar, S., Raubenheimer, B., Herbers, T. H. C. and Gallagher, E. L. 1997. Spectral evolution of shoaling and breaking waves. Journal of Geophysical Research, 102, 15797–15805.
Felton, E. A. and Crook, K. A. W. 2003. Evaluating the impacts of huge waves on rocky shorelines: an essay review of the book ‘Tsunami – The Underated Hazard’. Marine Geology, 197, 1–12.
Fine, I. V., Rabinovich, A. B., Bornhold, B. D., Thomson, R. E. and Kulikov, E. A. 2004. The Grand Banks landslide-generated tsunami of November 18, 1929: preliminary analysis and numerical modeling. Marine Geology, 215, 45–57.
Fredsǿe, J. and Deigaard, R. 1992. Mechanics of Coastal Sediment Transport. World Scientific, Singapore, 368 pp.
Galloway, J. S., Collins, M. B. and Moran, A. D. 1989. Onshore/offshore wind influence on breaking waves: An empirical study. Coastal Engineering, 13, 305–325.
Galvin, C. J. 1968. Breaker type classification on three laboratory beaches. Journal of. Geophysical Research, 73, 3651–3659.
Galvin, C. J., 1972. Wave breaking in shallow water. In Meyer, R. E. (ed.). Waves on Beaches and Resulting Sediment Transport. Academic, New York, pp. 413–455.
Greenwood, B. and McGillivray, D. G. 1978. Theoretical model of the littoral drift system in the Toronto waterfront, Lake Ontario. Journal of Great Lakes Research, 4, 84–102.
Guza, R. T. and Inman, D. L. 1975. Edge waves and beach cusps. Journal of Geophysical Research, 80, 2997–3012
Haller, M. E., Putrevu, U., Oltman-Shay, J. and Dalrymple, R. A. 1999. Wave group forcing of low frequency surf zone motion. Coastal Engineering Journal, 41, 121–136.
Holman, R. A. 1983. Edge waves and the configuration of the shoreline. Chapter 2 in Komar, P. D. (ed.), Handbook of Coastal Processes and Erosion. CRC Press, Boca Raton, FL, pp. 21–33.
Holman, R. A. and Sallenger, A. H. 1985. Set-up and swash on a natural beach. Journal of Geophysical Research, 90, 945–953.
Hsu, T. W., Hsu, J. R-C., Weng, W-K., Wang, S-K. and Ou, S-H. 2006. Wave setup and setdown generated by obliquely incident waves. Coastal Engineering, 53, 865–877.
Huntley, D. A. and Kim, C. S. 1984. Is surf beat forced or free?Proceedings of the 19th International Conference on Coastal Engineering, ASCE, pp. 871–885.
Huntley, D. A., Guza, R. T. and Thornton, E. B. 1981. Field observations of surf beat. 1. Progressive edge waves. Journal of Geophysical Research, 86, 6451–6466.
Iribarren, C. R. and Nogales, C., 1949. Protection des Ports., XV11 International Navigation Congress, Section ii, Comm. 4, 31–80.
Jackson, L. E., Barrie, J. V., Forbes, D. L., Shaw, J., Manson, G. K. and Schmidt, M. 2005. Effects of the 26 December 2004 Indian Ocean Tsunami in the Republic of Seychelles. Geological Survey of Canada, Open File 4539, 73 pp.
Karambas, T. V. and Koutitas, C. 2002. Surf and swash zone morphology evolution induced by non-linear waves. Journal of Waterway, Port, Coastal and Ocean Engineering, 128, 102–113.
Karunarathna, H. and Chadwick, A. J. 2007. On low frequency waves in the surf and swash. Ocean Engineering, 34, 2115–2123.
Komar, P. D. 1998. Beach Processes and Sedimentation, 2nd edn., Prentice-Hall, NJ, 544 pp.
Kortweg, D. J. and Vries, G. 1895. On the change of form of long waves advancing in a rectangular canal, and on a new type of stationary wave. Philosphical Magazine, 39, 422–443.
Lawrence, P. L. and Davidson-Arnott, R. G. D. 1997. Alongshore wave energy and sediment transport on south-eastern Lake Huron, Ontario, Canada. Journal of Coastal Research, 13, 1004–1015.
Lay, T., Kanamori, H., Ammon, C. J. and 11 others 2005. The great Sumatra Andaman earthquake of 26 December 2004. Science, 208, 1127–1133.
Lippmann, T. C., Brookins, A. H. and Thornton, E. B. 1996. Wave energy transformation on natural profiles. Coastal Engineering, 27, 1–20.
Longuett-Higgins, M. S. and Stewart, R. W. 1962. Radiation stresses and mass transport in gravity waves with applications to surf beat. Journal of Fluid Mechanics, 13, 481–504.
Longuett-Higgins, M. S. and Stewart, R. W. 1964. Radiation stress in water waves; a physical discussion with applications. Deep Sea Research, 11, 529–563.
Madsen, P. A., Sorensen, O. R. and Schaffer, H. A. 1997. Surf zone dynamics simulated by Boussinesq type model. Part 1. Model description and cross-shore motion of regular waves. Coastal Engineering, 32, 255–287.
Maramai, A., Graziani, L. and Tinti, S. 2005. Tsunamis in the Aeolian Islands (southern Italy): a review. Marine Geology, 21(5), 11–21.
Masselink, G. 1998. Field investigation of wave propagation over a bar and the consequent generation of secondary waves. Coastal Engineering, 33, 1–9.
Masselink, G. and Puleo, J. A. 2006. Swash zone morphodynamics. Continental Shelf Research, 26, 661–680.
May, J. P. 1974. WAVENRG: A computer program to determine the dissipation in shoaling water waves with examples from coastal Florida. In Tanner, W. F. (ed.) Sediment Transport in the Nearshore Zone. Coastal Research Notes, Department of Geology, University of Florida, 22–80.
Miller, R. L. 1976. Role of vortices in surf zone prediction: sedimentation and wave forces. In Davis, R. A. and Ethington, R. L. (eds.), Beach and Nearshore Sedimentation. S.E.P.M. Special Publication, 24, 92–114.
Morton, R. A., Goff, J. R. and Nichol, S. L. 2008. Hydrodynamic implications of textural trends in sand deposits of the 2004 tsunami in Sri Lanka. Sedimentary Geology, 207, 56–64.
Morton, R. A., Gelfenbaum, G. and Jaffe, B. E. 2007. Physical criteria for distinguishing sandy tsunami and storm deposits using modern examples. Sedimentary Geology, 200, 184–207.
Munk, W. H., 1949. The solitary wave theory and its application to surf problems. New York Academy of Science, 51, 376–424.
Munk, W. H. and Traylor, M. A. 1947. Refraction of ocean waves; a process linking underwater topography to beach erosion. Journal of Geology, 55, 1–26.
Okazaki, S-I and Sunamura, T. 1991. Re-examination of breaker type classification on uniformly inclined laboratory beaches. Journal of Coastal Research, 7, 559–564.
Paris, R., Lavigne, F., Wassmer, P. and Sartohadi, J. 2007. Coastal sedimentation associated with the December 26, 2004 tsunami in Lhok Nga, west Banda Aceh (Sumatra, Indonesia). Marine Geology, 238, 93–106.
Peregrine, D. H. 1983. Breaking waves on beaches. Annual Review of Fluid Mechanics, 15, 149–178.
Ruessink, B. G., Walstra, D. J. R. and Southgate, H. N. 2003. Calibration and verification of a parametric wave model on barred beaches. Coastal Engineering, 48, 139–149.
Stokes, G. G. 1847. On the theory of oscillatory waves. Transactions of the Cambridge Philosophical Society, 8, 441–445.
Sunamura, T. 1992. Geomorphology of Rocky Coasts. Wiley, Chichester, 302 pp.
Svendsen, I. A. 1984. Wave heights and set-up in a surf zone. Coastal Engineering, 8, 303–329.
Svendsen, I. A., Madsen, P. A. and Buhr Hansen, J. 1978. Wave characteristics in the surf zone. Proceedings of the 16th Coastal Engineering Conference, ASCE, 520–539.
Svendsen, I. A. and Veeramony, J. 2001. Wave breaking in wave groups. Journal of Waterway, Port, Coastal, and Ocean Engineering, 127, 200–212.
Symonds, G., Huntley, D. A. and Bowen, A. J. 1982. Long wave generation by a time-varying breakpoint. Journal of Geophysical Research, 87, 492–498.
Thornton, E. B. and Guza, R. T. 1982. Energy saturation and phase speeds measured on a natural beach. Journal of Geophysical Research, 87, 9499–9508.
Ting, F. C. K. and Kirby, J. T. 1995. Dynamics of surf-zone turbulence in a strong plunging breaker. Coastal Engineering, 24, 177–204.
Tucker, M. J. 1950. Surfbeats: Sea waves of 1 to 5 minutes period. Proceedings of the Royal Society of London A, 202, 565–573.
Umitsu, M., Tanavud, C. and Patanakanog, B. 2007. Effects of landforms on tsunami flow in the plains of Banda Aceh, Indonesia, and Nam Khem, Thailand. Marine Geology, 242, 141–153.
Veeramony, J. and Svensen, I. A. 2000. The flow in surf-zone waves. Coastal Engineering, 39, 93–122.
Vincent, C. L., Demirbilek, Z. and Weggel, J. R., 2002. Estimation of nearshore waves. Chapter 3 in EM 1110–2–1100 Part 2, Coastal Engineering Manual, US Army Corps of Engineers, 41pp.
Weishar, L. L. and Byrne, R. J. 1978. Field study of breaking wave characteristics. Proceedings of the 16th Coastal Engineering Conference, ASCE, pp. 487–506.
Wilson, W. S. 1966. A method for calculating and plotting surface wave rays. US Army Corps of Engineers. CERC Technical Memorandum 17.
Wright, L. D. and Short, A. D. 1984. Morphodynamic variability of surf zones and beaches: a synthesis. Marine Geology, 56, 93–118.
Young, R. W. and Bryant, E. A. 1992. Catastrophic wave erosion on the southeastern coast of Australia: Impact of the Lanai tsunami ca. 105 ka? Geology, 20, 199–202.