Progress of edge waves research

1.
Key Laboratory of Coastal Disaster and Protection, Ministry of Education, College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China
2.
China Harbour Engineering Company Limited, Beijing 100027, China

Received Date: 2022-03-30
Rev Recd Date: 2022-07-27

Available Online: 2022-11-10

Publish Date: 2023-01-17

Abstract

Abstract

Due to the effect of refraction, a special phenomenon that propagates along the shoreline occurs during the nearshore propagation of waves, which are called edge waves. The edge waves propagate parallel to the shoreline, and their amplitude is the largest at the shoreline, and its amplitude decreases exponentially in the direction away from the shoreline, and their energy is limited to a distance of one wavelength from the coast. So the edge waves have an important impact on the engineering and landforms of the near-shore area. This paper expounds on the research history and research progress of edge waves and mainly introduces the following aspects: (1) the theory of edge waves based on different governing equations and different terrains; (2) the actual observed edge wave characteristics; (3) the wave-making method of edge waves in the physical model test and the observed edge wave characteristics; (4) the application of numerical simulation methods in the study of edge waves. Finally, the future research trend of edge waves is presented.
- edge waves,
- theoretical derivation,
- field observation,
- physical modelling experiments,
- numerical simulation,
- generation mechanism

FullText(HTML)

References(54)

References

[1]	Fujima K, Dozono R, Shigemura T. Generation and propagation of tsunami accompanying edge waves on a uniform sloping shelf[J]. Coastal Engineering Journal, 2000, 42(2): 211−236. doi: 10.1142/S0578563400000109
[2]	Koyano K, Takabatake T, Esteban M, et al. Influence of edge waves on tsunami characteristics along Kujukuri Beach, Japan[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 2021, 147(1): 04020049. doi: 10.1061/(ASCE)WW.1943-5460.0000617
[3]	Sallenger A H Jr, Holman R A, Birkemeier W A. Storm-induced response of a nearshore-bar system[J]. Marine Geology, 1985, 64(3/4): 237−257.
[4]	González F I, Satake K, Boss E F, et al. Edge wave and non-trapped modes of the 25 April 1992 cape Mendocino tsunami[J]. Pure and Applied Geophysics, 1995, 144(3): 409−426.
[5]	Bowen A J, Inman D L. Edge waves and crescentic bars[J]. Journal of Geophysical Research, 1971, 76(36): 8662−8671. doi: 10.1029/JC076i036p08662
[6]	Guza R T, Inman D L. Edge waves and beach cusps[J]. Journal of Geophysical Research, 1975, 80(21): 2997−3012. doi: 10.1029/JC080i021p02997
[7]	Almar R, Coco G, Bryan K R, et al. Video observations of beach cusp morphodynamics[J]. Marine Geology, 2008, 254(3/4): 216−223.
[8]	Stokes G G. On the Theory of Oscillatory Waves[M]. Printed at the Pitt Press, 1847: 314−326.
[9]	Eckart C. Surface waves on water of variable depth[R]. Scripps: University of California, 1951: 99.
[10]	Ursell F. Edge waves on a sloping beach[J]. Proceedings of the Royal Society A: Mathematical, and Physical Sciences, 1952, 214(1116): 79−97.
[11]	Rockliff N. Finite amplitude effects in free and forced edge waves[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1978, 83(3): 463−479. doi: 10.1017/S030500410005475X
[12]	Gallagher B. Generation of surf beat by non-linear wave interactions[J]. Journal of Fluid Mechanics, 1971, 49(1): 1−20. doi: 10.1017/S0022112071001897
[13]	Guza R T, Davis R E. Excitation of edge waves by waves incident on a beach[J]. Journal of Geophysical Research, 1974, 79(9): 1285−1291. doi: 10.1029/JC079i009p01285
[14]	Guza R T, Bowen A J. Finite amplitude edge waves[J]. Journal of Marine Research, 1976, 34(2): 269−293.
[15]	Whitham G B. Nonlinear effects in edge waves[J]. Journal of Fluid Mechanics, 1976, 74(2): 353−368. doi: 10.1017/S0022112076001833
[16]	Minzoni A A. Nonlinear edge waves and shallow-water theory[J]. Journal of Fluid Mechanics, 1976, 74(2): 369−374. doi: 10.1017/S0022112076001845
[17]	Schäuffer H A. Edge waves forced by short-wave groups[J]. Journal of Fluid Mechanics, 1994, 259: 125−148. doi: 10.1017/S0022112094000066
[18]	Blondeaux P, Vittori G. The nonlinear excitation of synchronous edge waves by a monochromatic wave normally approaching a plane beach[J]. Journal of Fluid Mechanics, 1995, 301: 251−268. doi: 10.1017/S0022112095003880
[19]	Hong Guangwen, Zhang Yu. Second-order analytic solutions of nonlinear interactions of edge waves on a plane sloping bottom[J]. China Ocean Engineering, 2010, 24(1): 1−14.
[20]	Vittori G, Blondeaux P, Coco G, et al. Subharmonic edge wave excitation by narrow-band, random incident waves[J]. Journal of Fluid Mechanics, 2019, 868: R4. doi: 10.1017/jfm.2019.214
[21]	Greenspan H P. The generation of edge waves by moving pressure distributions[J]. Journal of Fluid Mechanics, 1956, 1(6): 574−592. doi: 10.1017/S002211205600038X
[22]	Liu P L F, Monserrat S, Marcos M. Analytical simulation of edge waves observed around the Balearic Islands[J]. Geophysical Research Letters, 2002, 29(17): 1847.
[23]	Seo S N, Liu P L F. Edge waves generated by atmospheric pressure disturbances moving along a shoreline on a sloping beach[J]. Coastal Engineering, 2014, 85: 43−59. doi: 10.1016/j.coastaleng.2013.12.002
[24]	Seo S N, Liu P L F. Edge waves generated by the landslide on a sloping beach[J]. Coastal Engineering, 2013, 73: 133−150. doi: 10.1016/j.coastaleng.2012.10.008
[25]	Ball F K. Edge waves in an ocean of finite depth[J]. Deep Sea Research and Oceanographic Abstracts, 1967, 14(1): 79−88. doi: 10.1016/0011-7471(67)90030-7
[26]	Clarke D J. High frequency edge waves on an exponential shelf[J]. Deutsche Hydrographische Zeitschrift, 1973, 26(6): 265−271. doi: 10.1007/BF02226668
[27]	Evans D V, Mciver P. Edge waves over a shelf: full linear theory[J]. Journal of Fluid Mechanics, 1984, 142: 79−95. doi: 10.1017/S0022112084001002
[28]	Louis J P, Clarke D J. Exact edge wave solutions for some generalised exponential shelf topographies[J]. The ANZIAM Journal, 1986, 27(3): 316−326.
[29]	Wang Gang, Dong Guohai, Perlin M, et al. An analytic investigation of oscillations within a harbor of constant slope[J]. Ocean Engineering, 2011, 38(2/3): 479−486.
[30]	Shao Dong, Feng Weibing, Feng Xi. An analytical investigation for oscillations in a harbor of a parabolic bottom[J]. Journal of Marine Science and Technology, 2016, 21(3): 416−425. doi: 10.1007/s00773-015-0363-9
[31]	Shao Dong, Feng Xi, Feng Weibing, et al. Harbor oscillations on a piecewise bottom of two different slopes[J]. Journal of Marine Science and Technology, 2017, 22(4): 633−654. doi: 10.1007/s00773-017-0437-y
[32]	Zhang D, Wang G, Feng X, et al. Analytical and numerical investigation of edge waves near a vertical breakwater over a convex bottom[J]. Ocean Engineering, 2022, 266: 112923.
[33]	Donn W L, Ewing M. Stokes’ edge waves in Lake Michigan[J]. Science, 1956, 124(3234): 1238−1242. doi: 10.1126/science.124.3234.1238
[34]	Munk W, Snodgrass F, Gilbert F. Long waves on the continental shelf: an experiment to separate trapped and leaky modes[J]. Journal of Fluid Mechanics, 1964, 20(4): 529−554. doi: 10.1017/S0022112064001392
[35]	Huntley D A, Bowen A J. Field observations of edge waves[J]. Nature, 1973, 243(5403): 160−162. doi: 10.1038/243160a0
[36]	Huntley D A, Guza R T, Thornton E B. Field observations of surf beat: 1. Progressive edge waves[J]. Journal of Geophysical Research, 1981, 86(C7): 6451−6466. doi: 10.1029/JC086iC07p06451
[37]	Oltman-Shay J, Guza R T. Infragravity edge wave observations on two California beaches[J]. Journal of Physical Oceanography, 1987, 17(5): 644−663. doi: 10.1175/1520-0485(1987)017<0644:IEWOOT>2.0.CO;2
[38]	Aagaard T. Multiple-bar morphodynamics and its relation to low-frequency edge waves[J]. Journal of Coastal Research, 1991, 7(3): 801−813.
[39]	Yeh H H. Nonlinear progressive edge waves: their instability and evolution[J]. Journal of Fluid Mechanics, 1985, 152: 479−499. doi: 10.1017/S0022112085000799
[40]	Liu P L F, Yeh H, Lin P, et al. Generation and evolution of edge-wave packets[J]. Physics of Fluids, 1998, 10(7): 1635−1657. doi: 10.1063/1.869682
[41]	Bowen A J, Inman D L. Rip currents: 2. Laboratory and field observations[J]. Journal of Geophysical, 1969, 74(23): 5479−5490. doi: 10.1029/JC074i023p05479
[42]	Guza R T, Bowen A J. Resonant interactions for waves breaking on a beach[J]. Coastal Engineering Proceedings, 1976, 1(15): 560−579.
[43]	Wang Gang, Zheng Jinhai, Maa J P Y, et al. Numerical experiments on transverse oscillations induced by normal-incident waves in a rectangular harbor of constant slope[J]. Ocean Engineering, 2013, 57: 1−10. doi: 10.1016/j.oceaneng.2012.09.010
[44]	Shao Dong, Feng Xi, Feng Weibing. Numerical investigation of oscillations within a harbor of parabolic bottom induced by water surface disturbances[J]. Applied Ocean Research, 2016, 59: 153−164. doi: 10.1016/j.apor.2016.05.005
[45]	Sheremet A, Guza R T. A weakly dispersive edge wave model[J]. Coastal Engineering, 1999, 38(1): 47−52. doi: 10.1016/S0378-3839(99)00022-8
[46]	Wang Gang, Sun Zhongbin, Gao Junliang, et al. Numerical study of edge waves using extended Boussinesq equations[J]. Water Science and Engineering, 2017, 10(4): 295−302. doi: 10.1016/j.wse.2017.12.002
[47]	Lu Yang, Feng Weibing, Zhang Yu, et al. A numerical model for edge waves on a compound slope[J]. China Ocean Engineering, 2017, 31(2): 167−172. doi: 10.1007/s13344-017-0020-7
[48]	Yankovsky A E. Large-scale edge waves generated by hurricane landfall[J]. Journal of Geophysical Research, 2009, 114(C3): C03014.
[49]	An Chao, Liu P L F, Seo S N. Large-scale edge waves generated by a moving atmospheric pressure[J]. Theoretical and Applied Mechanics Letters, 2012, 2(4): 042001. doi: 10.1063/2.1204201
[50]	Niu Xiaojing. Conditions for the occurrence of notable edge waves due to atmospheric disturbances[J]. Applied Ocean Research, 2020, 101: 102255. doi: 10.1016/j.apor.2020.102255
[51]	Lynett P, Liu P L F. A numerical study of the run-up generated by three-dimensional landslides[J]. Journal of Geophysical Research, 2005, 110(C3): C03006.
[52]	Sammarco P, Renzi E. Landslide tsunamis propagating along a plane beach[J]. Journal of Fluid Mechanics, 2008, 598: 107−119. doi: 10.1017/S0022112007009731
[53]	Wang Gang, Dong Guohai, Perlin M, et al. Numerical investigation of oscillations within a harbor of constant slope induced by seafloor movements[J]. Ocean Engineering, 2011, 38(17/18): 2151−2161.
[54]	Shao Dong, Feng Xi, Feng Weibing, et al. Numerical investigation of oscillations induced by submerged sliding masses within a harbor of constant slope[J]. Applied Ocean Research, 2017, 63: 49−64. doi: 10.1016/j.apor.2017.01.002