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Siberian Journal of Numerical Mathematics

2015 year, number 4

The assessment of tsunami heights above the bottom slope within the wave-ray approach

An.G. Marchuk
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Lavrentieva, 6, Novosibirsk, 630090
Keywords: распространение цунами, уравнения мелкой воды, волновой луч, кинематика волнового фронта, tsunami propagation, shallow-water equations, wave ray, wave front kinematics


In this paper, the kinematics of the tsunami wave ray and wave front above an uneven bottom is studied. The formula to determine the wave height along a ray tube is obtained. The exact analytical solution for the wave-ray trajectory above the bottom slope is derived. This solution gives the possibility to determine within the wave-ray approach the tsunami wave heights in an area with a sloping bottom relief. The distribution of the wave-height maxima in the area with the sloping bottom is compared to the one obtained by the numerical computation with a shallow-water model.