The assessment of tsunami heights above the parabolic bottom relief within the wave-ray approach
An.G. Marchuk
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentieva 6, Novosibirsk, 630090, Russia
Keywords: распространение цунами, уравнения мелкой воды, волновой луч, кинематика волнового фронта, tsunami propagation, shallow-water equations, wave ray, wavefront kinematics
Abstract
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.
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