headerpos: 12198
 
 
 

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
Publisher
Journal Information
» Editorial Board
» Editorial Policy
» Archival Policy
» Article Publication Charges
» Copyright and Licensing Policy
Guidelines for Authors
» For Authors
» Instructions to Authors
» LaTex style files
Guidelines for Reviewers
» For Reviewers
» Review Form
Open Access
List of Issues
» 2019
» 2018
» 2017
» 2016
» 2015
Vol. 64, Issue 4S
Vol. 64, Issue 4
Vol. 64, Issue 3S
Vol. 64, Issue 3
Vol. 64, Issue 2
Vol. 64, Issue 1S
Vol. 64, Issue 1
» 2014
» 2013
» 2012
» 2011
» 2010
» 2009
» 2008
» Back Issues Phys. Math.
» Back Issues Chemistry
» Back issues (full texts)
  in Google. Phys. Math.
» Back issues (full texts)
  in Google. Chemistry
» Back issues (full texts)
  in Google Engineering
» Back issues (full texts)
  in Google Ecology
» Back issues in ETERA Füüsika, Matemaatika jt
Subscription Information
» Prices
Internet Links
Support & Contact
Publisher
» Staff
» Other journals

Advantages and limitations of the nonlinear Schrödinger equation in describing the evolution of nonlinear water-wave groups; pp. 356–360

(Full article in PDF format) doi: 10.3176/proc.2015.3S.05


Authors

Lev Shemer

Abstract

The nonlinear Schrödinger (NLS) equation is a popular and relatively simple model used extensively to describe the evolution of nonlinear water-wave groups. It is often applied in relation to the appearance of extremely steep (freak, or rogue) waves in the ocean. The limits of the applicability of the NLS equation, and in particular the relevance of the model to rogue waves, are examined here on the basis of quantitative and qualitative comparison with an experiment.

Keywords

nonlinear water waves, nonlinear Schrödinger equation, breaking waves, rogue waves, breathers, Peregrine breather

References

  1. Shrira , V. I. and Geogjaev , V. V. What makes the Peregrine soliton so special as a prototype of freak waves? J. Eng. Math. , 2010 , 67 , 11–22.
http://dx.doi.org/10.1007/s10665-009-9347-2

  2. Peregrine , D. H. Water waves , nonlinear Schrödinger equations and their solutions. J. Austr. Math. Soc. , Ser. B. , 1983 , 25 , 16–43.

  3. Chabchoub , A. , Hoffmann , N. P. , and Akhmediev , N. Rogue wave observation in a water wave tank. Phys. Rev. Lett. , 2011 , 106 , 204502.
http://dx.doi.org/10.1103/PhysRevLett.106.204502

  4. Shemer , L. and Alperovich , L. Peregrine breather revisited. Phys. Fluids , 2013 , 25 , 051701.
http://dx.doi.org/10.1063/1.4807055

  5. Dysthe , K. B. Note on the modification of the nonlinear Schrödinger equation for application to deep water waves. Proc. Roy. Soc. London , 1979 , A369 , 105–114.
http://dx.doi.org/10.1098/rspa.1979.0154

  6. Lo , E. and Mei , C. C. A numerical study of water-wave modulation based on higher-order nonlinear Schrödinger equation. J. Fluid Mech. , 1985 , 150 , 395–416.
http://dx.doi.org/10.1017/S0022112085000180

  7. Kit , E. and Shemer , L. Spatial versions of the Zakharov and Dysthe evolution equations for deep-water gravity waves. J. Fluid Mech. , 2002 , 450 , 201–205.
http://dx.doi.org/10.1017/S0022112001006498

  8. Zakharov , E. Stability of periodic waves of finite amplitude on a surface of deep fluid. J. Appl. Mech. Tech. Phys. , (English transl.) , 1968 , 2 , 190–194.

  9. Shemer , L. , Goulitski , K. , and Kit , E. Evolution of wide-spectrum unidirectional wave groups in a tank: an experimental and numerical study. Eur. J. Mech. B/Fluids , 2007 , 26 , 193–219.
http://dx.doi.org/10.1016/j.euromechflu.2006.06.004

10. Stiassnie , M. Note on the modified Schrödinger equation for deep water waves. Wave Motion , 1984 , 6 , 431–433.
http://dx.doi.org/10.1016/0165-2125(84)90043-X

11. Shemer , L. , Kit , E. , Jiao , H. , and Eitan , O. Experiments on nonlinear wave groups in intermediate water depth. J. Waterway , Port , Coastal & Ocean Engineering , 1998 , 124 , 320–327.
http://dx.doi.org/10.1061/(ASCE)0733-950X(1998)124:6(320)

12. Slunyaev , V. V. and Shrira , V. I. On the highest non-breaking wave in a group: fully nonlinear water wave breathers versus weakly nonlinear theory. J. Fluid Mech. , 2013 , 735 , 203–248.
http://dx.doi.org/10.1017/jfm.2013.498

13. Shemer , L. and Liberzon , D. Lagrangian kinematics of steep waves up to the inception of a spilling breaker. Phys. Fluids , 2014 , 26 , 016601.
http://dx.doi.org/10.1063/1.4860235

 
Back

Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December