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Inverse non-linear problem of the long-wave run-up on coast

Journal of Ocean Engineering and Marine Energy. 2024. Vol. 10. P. 941–952.
Rybkin A., Pelinovsky E., Bobrovnikov O., Palmer N., Pniushkova E., Abramowicz D.

The study of the process of catastrophic tsunami-type waves on the coast makes it possible to determine the destructive force of waves on the coast. In hydrodynamics, the one-dimensional theory of the run-up of non-linear waves on a flat slope has gained great popularity, within which rigorous analytical results have been obtained in the class of non-breaking waves. In general, the result depends on the characteristics of the wave approaching (or generated on) the slope, which is usually not known in the measurements. Here, we describe a rigorous method for recovering the initial displacement in a source localised in an inclined power-shaped channel from the characteristics of a moving shoreline. The method uses the generalised Carrier–Greenspan transformation, which allows one-dimensional non-linear shallow-water equations to be reduced to linear ones. The solution is found in terms of Erdélyi–Kober integral operator. Numerical verification of our results is presented for the cases of a parabolic bay and an infinite plane beach.

Research target: Mathematics Earth Sciences
Language: English
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Keywords: нелинейная теория мелкой водыNonlinear shallow-water theory
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