Analytic Simulation To The Propagation Of Landslide Tsunami Around An Island With Quasi-idealized Water Depth

In this thesis, analytical simulation to the propagation of landslide tsunami around an axi-symmetrical quasi-idealized island is conducted, where the so-called quasi-idealized island means that the water depth pro?le is a power function of the radial distance plus a nonzero constant.In 2010, the landslide tsunamis around an axi-symmetrical conical island with quasiidealized water depth was studied by Sammarco and Renzi, where the water depth is a linear function of the radial distance. Sammarco and Renzi’s solution is in a closed form in terms of Bessel functions. In this thesis, the conical island is extended to an island with the water depth being a power function with arbitrary exponent including rational exponent. This leads to a more complex boundary valued problem and only a series solution can be constructed. By careful analysis to the problem, it is found that the Frobenius’ series solution converges only for the cases with the power exponent being integers 1 to 4. In the far ?eld, the analytical solution is a combination of the Bessel functions.As a validation, our solution with the power exponent being 1 is compared with Sammarco and Renzi’s solution and the agreement is quite well. Based on the present solution, the in?uence of the island parameters on the wave ampli?cation is investigated.