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Analytical solution for cylindrical propagation of tsunami in the ocean of variable depth
Wave Motion. 2026. Vol. 147. Article 103787.
This work presents a new analytical solution of the shallow water theory for cylindrical propagation of long tsunami-like waves in the basin of variable depth. Considered model cases are related to tsunami wave propagation from an asteroid fallen into the sea, or from underwater volcanic eruptions. The corresponding bottom geometries represent radially symmetric obstacles such as hills or holes on the sea bottom. Tsunami dynamics in these cases is discussed in detail. It is shown for the case of underwater hole that bathymetry h ∼ r-2 can compensate the wave attenuation due to its divergence resulting in the wave of constant amplitude. It is also shown that waves attenuate very fast along underwater hills leading to a local effect of tsunami. The proposed solutions can be used as benchmarks for validation of numerical models.
Keywords: tsunamiцунамианалитическое решениеanalytical solutionCylindrical wavesVariable bottom bathymetryцилиндрические волныпеременная батиметрия дна
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