Dispersive and Nondispersive Nonlinear Long Wave Transformations: Numerical and Experimental Results

  • Tomas TorsvikEmail author
  • Ahmed Abdalazeez
  • Denys Dutykh
  • Petr Denissenko
  • Ira Didenkulova
Part of the Mathematics of Planet Earth book series (MPE, volume 6)


The description of gravity waves propagating on the water surface is considered from a historical point of view, with specific emphasis on the development of a theoretical framework and equations of motion for long waves in shallow water . This provides the foundation for a subsequent discussion about tsunami wave propagation and runup on a sloping beach, and in particular the role of wave dispersion for this problem. Wave tank experiments show that wave dispersion can play a significant role for the propagation and wave transformation of wave signals that include some higher frequency components. However, the maximum runup height is less sensitive to dispersive effects, suggesting that runup height can be adequately calculated by use of nondispersive model equations.


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This work was supported by Estonian Research Council (ETAg) grant PUT1378. Authors also thank the PHC PARROT project No 37456YM, which funded the authors’ visits to France and Estonia and allowed this collaboration.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tomas Torsvik
    • 1
    • 2
    Email author
  • Ahmed Abdalazeez
    • 3
  • Denys Dutykh
    • 4
  • Petr Denissenko
    • 5
  • Ira Didenkulova
    • 3
    • 6
  1. 1.Norwegian Polar InstituteFram CentreTromsøNorway
  2. 2.Geophysical InstituteUniversity of BergenBergenNorway
  3. 3.Department of Marine SystemsSchool of Science, Tallinn University of TechnologyTallinnEstonia
  4. 4.University Grenoble AlpesUniversity Savoie Mont Blanc, CNRS, LAMAChambéryFrance
  5. 5.School of EngineeringUniversity of WarwickCoventryUK
  6. 6.Nizhny Novgorod Technical University n.a. R.E. AlekseevNizhny NovgorodRussia

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