Tsunami amplification phenomena.

Summary This thesis is divided into four parts. In the first part, I will present our work on long wave run-up and resonance amplification phenomena. Using numerical simulations based on the nonlinear shallow water equations, we show that for monochromatic waves of normal incidence on a sloping beach, resonant amplification of the run-up occurs when the input wave length is 5.2 times greater than the beach length. We also show that this resonant run-up amplification can be observed from multiple wave profiles. However, the resonant run-up amplification is not limited to infinite sloping beaches. By varying the bathymetric profile, resonance is also present for piecewise linear bathymetries and for realistic bathymetries. In the second part, I present a new analytical solution to study the propagation of non-point source generated tsunamis over a constant depth using linear shallow water wave theory. The solution, based on separation of variables and a double Fourier transform in space, is accurate, easy to implement and allows the study of realistic wave shapes such as N-waves. In the third part, I study the effect of localized protrusions on the generation of long waves. Even when the final displacement is known from seismic analysis, the deforming seafloor may have relief such as mountains and faults. The effect of bathymetry on surface wave generation is studied analytically by solving the linear shallow water equations with for. We find that as the rim height increases, partial wave trapping reduces the wave height in the far field, while amplifying it above the rim. I will also briefly present a solution of the same equation forced over a cone. Finally, in the last part, we will see if small islands can protect nearby coasts from tsunamis as is widely accepted by local communities. Recent findings on the 2010 Mentawai Islands tsunami show an amplified run-up on coastal areas behind small islands, compared to the run-up on adjacent locations, which are not influenced by the presence of islands. We will investigate the conditions for this run-up amplification by numerically solving the equations in nonlinear shallow water. The experimental setup is governed by five physical parameters. The objective is twofold: Find the maximum run-up amplification with a minimum number of simulations. We present a recently developed active experimental design based on Gaussian processes, which significantly reduces the computational cost. After running two hundred simulations, we find that in none of the cases considered does the island provide protection to the coastal area behind it. On the contrary, we measured an amplification of the run-up on the beach behind it compared to a lateral position on the beach not directly affected by the presence of the island. This amplification reached a maximum factor of 1.7. Thus, small islands near the mainland act as amplifiers of the long waves in the area directly behind them and not as natural barriers as was commonly believed until now.