Geodesic
The assessment of tsunami heights above the parabolic bottom relief within the wave-ray approach
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 1, pp. 23-35

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In this paper, the kinematics of the tsunami wave ray and the wavefront above an uneven bottom is studied. The formula to determine the wave height along a ray tube has been obtained. The exact analytical solution for the wave-ray trajectory above the parabolic bottom topography has been derived. Within the wave-ray approach this solution gives the possibility to determine the tsunami wave heights in an area with a parabolic bottom relief. The distribution of the wave-height maxima in the area with the parabolic bottom was compared to the one obtained by the numerical computation with a shallow-water model. 
@article{SJVM_2017_20_1_a2,
     author = {An. G. Marchuk},
     title = {The assessment of tsunami heights above the parabolic bottom relief within the wave-ray approach},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {23--35},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2017_20_1_a2/}
}
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An. G. Marchuk. The assessment of tsunami heights above the parabolic bottom relief within the wave-ray approach. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 1, pp. 23-35. http://geodesic.mathdoc.fr/item/SJVM_2017_20_1_a2/