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.
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Acknowledgements
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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Torsvik, T., Abdalazeez, A., Dutykh, D., Denissenko, P., Didenkulova, I. (2019). Dispersive and Nondispersive Nonlinear Long Wave Transformations: Numerical and Experimental Results. In: Berezovski, A., Soomere, T. (eds) Applied Wave Mathematics II. Mathematics of Planet Earth, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-030-29951-4_3
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