Dispersive and non-dispersive nonlinear long wave transformations: numerical and experimental results

Abstract

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.

Keywords

Bibliographic record

BibTeX Citation

@incollection{Torsvik_2019_dispersive_and_nondispersive,
  title = {Dispersive and non-dispersive nonlinear long wave transformations: numerical and experimental results},
  author = {Torsvik, T. and Abdalazeez, A. and Dutykh, D. and Denissenko, P. and Didenkulova, I.},
  booktitle = {Applied Wave Mathematics II},
  editor = {Berezovski, A. and Soomere, T.},
  publisher = {Springer},
  year = {2019},
  pages = {41--66},
  doi = {10.1007/978-3-030-29951-4_3},
  url = {https://hal.archives-ouvertes.fr/hal-02289778/},
  series = {Mathematics of Planet Earth},
  volume = {6},
  isbn = {978-3-030-29950-7},
  keywords = {Mathematics, Partial Differential Equations, Applications of Mathematics, Acoustics, Numerical Analysis, Classical Electrodynamics, Mathematical Methods in Physics}
}