Chin. Phys. Lett.  2019, Vol. 36 Issue (9): 090501    DOI: 10.1088/0256-307X/36/9/090501
GENERAL |
Formation of Square-Shaped Waves in the Biscay Bay
Xin Li1,2, Wen-Hao Xu1,2, Dong-Ming Chen1,2, Li-Ke Cao1,2, Zhan-Ying Yang1,2**
1School of Physics, Northwest University, Xi'an 710069
2Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710069
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Xin Li, Wen-Hao Xu, Dong-Ming Chen et al  2019 Chin. Phys. Lett. 36 090501
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Abstract Recently, a report from Elite Readers suggested that a strange phenomenon of 'square-shaped waves' had occurred at the beaches of the Isle of Rhe in the Bay of Biscay. Based on the hydrological and geological data of the Bay of Biscay, we find that the special phenomenon is closely related to a solitary wave that can be described by the shallow water wave equation. We discuss the formation mechanisms of the square-shaped waves by the Kadomtsev–Petviashvili equation. The combination of exact solutions and actual condition provides the simulated initial state. We then reproduce a square-shaped structure by a numerical method and obtain the result consistent with the observed picture from media. Our work enriches public understanding of strange water waves and has great significance for tourism development and shipping transportation.
Received: 26 April 2019      Published: 23 August 2019
PACS:  05.45.Yv (Solitons)  
  92.10.Hm (Ocean waves and oscillations)  
  47.35.-i (Hydrodynamic waves)  
Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11875220 and 11425522.
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https://cpl.iphy.ac.cn/10.1088/0256-307X/36/9/090501       OR      https://cpl.iphy.ac.cn/Y2019/V36/I9/090501
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Xin Li
Wen-Hao Xu
Dong-Ming Chen
Li-Ke Cao
Zhan-Ying Yang
[1]Russell J S 1844 Report 14th Meeting of the British Association for the Advancement of Science
[2]Kadomtsev B B and Petviashvili V I 1970 Sov. Phys. Dokl. 15 539
[3]Miles J W 1980 Annu. Rev. Fluid Mech. 12 11
[4]Korteweg D and de Vries G 1895 Philos. Mag. 39 422
[5]Ankiewicz A et al 2019 Phys. Rev. E 99 050201
[6]Zabusky N J and Kruskal M D 1965 Phys. Rev. Lett. 15 240
[7]Ablowitz M J and Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (New York: Cambridge University Press)
[8]Hasegawa A and Kodama Y 1995 Solitons in Optical Communications (Oxford: Oxford University Press)
[9]Sinkala Z 2006 J. Theor. Biol. 241 919
[10]Ma J L and Ma F T 2007 Front. Phys. Chin. 2 368
[11]Kharif C, Pelinovsky E and Slunyaev A 2009 Rogue Waves in the Ocean. Advances in Geophysical and Environmental Mechanics and Mathematics
[12]Dysthe K B and Trulsen K 1999 Phys. Scr. 82 48
[13]Osborne A R et al 2000 Phys. Lett. A 275 386
[14]Onorato M et al 2001 Phys. Rev. Lett. 86 5831
[15]Garrett C and Gemmrich J 2009 Phys. Today 62 62
[16]Peregrine D H 1983 J. Aust. Math. Soc. Ser. B Appl. Math. 25 16
[17]Shrira V I and Geogjaev V V 2010 J. Eng. Math. 67 11
[18]Wang X et al 2014 Chin. Phys. Lett. 31 090201
[19]Duan L et al 2016 Chin. Phys. Lett. 33 010501
[20]Dudley J M et al 2014 Nat. Photon. 8 755
[21]Zhao F et al 2012 Ann. Phys. 327 2085
[22]Bludov Y V et al 2009 Phys. Rev. A 80 033610
[23]http://www.elitereaders.com/rare-dangerous-square-shaped-waves/
[24]Chakravarty S and Kodama Y 2009 Stud. Appl. Math. 123 83
[25]Bourgault D et al 2016 Nat. Commun. 7 13606
[26]Hirota R 1973 J. Math. Phys. 14 810
[27]Ablowitz M J and Villarroel J 1997 Phys. Rev. Lett. 78 570
[28]O'Driscoll K and Levine M 2017 Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 13 749
[29]Yang J 2010 Nonlinear Waves in Integrable and Nonintegrable Systems (Philadelphia: Siam)
[30]Baines P G 1982 Deep-Sea Res. Pt. A 29 307
[31]Azevedo A da Silva J C B and New A L 2006 Deep-Sea Res. Pt. I 53 927
[32]Wheeler W H 1899 Nature 60 461
[33]Alford M H et al 2015 Nature 521 65
[34]Fan D D et al 2014 Mar. Geol. 348 1
[35]Data sources https://www.ngdc.noaa.gov/
[36]Ku L F et al 1985 Science 230 69
[37]Huang X et al 2016 Sci. Rep. 6 30041
[38]Ablowitz M J and Baldwin D E 2012 Phys. Rev. E 86 036305
[39]Ablowitz M J 2011 Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons (New York: Cambridge University Press)
[40]Hirota R 2004 The Direct Method in Soliton Theory (New York: Cambridge University Press)
[41]Chakravarty S and Kodama Y 2008 Contemp. Math. 471 47
[42]Horowitz S and Zarmi Y 2015 Physica D 300 1
[43]Kao C Y and Kodama Y 2012 Math. Comput. Simul. 82 1185
[44]The picture is taken from www.veer.com
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