On the contribution of the horizontal sea-bed displacements into the tsunami generation process

The main reason for the generation of tsunamis is the deformation of the bottom of the ocean caused by an underwater earthquake. Usually, only the vertical bottom motion is taken into account while the horizontal co-seismic displacements are neglected in the absence of landslides. In the present study we propose a methodology based on the well-known Okada solution to reconstruct in more details all components of the bottom coseismic displacements. Then, the sea-bed motion is coupled with a three-dimensional weakly nonlinear water wave solver which allows us to simulate a tsunami wave generation. We pay special attention to the evolution of kinetic and potential energies of the resulting wave while the contribution of the horizontal displacements into wave energy balance is also quantified. Such contribution of horizontal displacements to the tsunami generation has not been discussed before, and it is different from the existing approaches. The methods proposed in this study are illustrated on the July 17, 2006 Java tsunami and some more recent events.Comment: 30 pages; 14 figures. Accepted to Ocean Modelling. Other authors papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

A fully nonlinear numerical method for modeling wave-current interactions

The presence of current in the ocean can significantly modify the characteristics of ocean waves, and it is considered as an important factor responsible for the occurrence of extreme waves, e.g., rogue waves, which are well known as great threats to ocean engineering practices. The magnitude and direction of ocean current normally vary spatially and ocean waves can become very large and steep. Accurate and efficient phase-revolved numerical methods of full y nonlinear wave-current interactions on a large scale in three dimensions (3D) are required to under stand their properties , but the existing phase-revolved methods are all based on the assumption of linear or weakly nonlinear interactions. This paper will address the issues and present a fully nonlinear numerical method to model the 3D interactions between waves and varying current on a large scale using a phase-revolved formulation . A new set of equations describing the three-dimensional, fully nonlinear interactions between waves and horizontally shearing current is proposed. They are derived by making no assumption on wave steepness or the order of wave- current interaction. The resulting new equations correctly describ e the free surface b oundary conditions by representing the fully nonlinear wave-current interactions , removing the limitation to the small wave steepness of the existing formulations in literature. On this basis, the recently developed Enhanced Spectral Boundary Integral (short as ESBI) method is further enhanced to be able to model the wave-current interactions using the new equations, by developing the appropriate procedure for dealing with the extra terms related to nonlinear wave-current interactions. The new equations are used as the prognostic equations for updating the free surface in time domain, and a fast converging iterative technique is employed to solve them. The robustness of the newly developed method is demonstrated through comparing with experimental data available in literature and good agreements are observed in the several different cases, including the 3D fully interaction between ocean waves and horizontally varying current. A comparison with a Higher Order Spectrum (HOS) method based on weak-nonlinear formulation of wave-current interaction is also made to confirm larger error does appear if the wave steepness is large. The method presented in the paper can be employed to simulate the real evolution of ocean waves on current in a phase-revolved way t o give deep insight s to the dynamics of wave-current interactions, which may not be done correctly by the existing methods so far

Probabilistic Hazard Assessment of Tsunamis Induced by the Translational Failure of Multiple Submarine Rigid Landslides

A numerical study aimed at probabilistically assessing the coastal hazard posed by tsunamis induced by one-dimensional submarine rigid landslides that experience translational failure is presented. The numerical model here utilized is the finite-difference recreation of a linear, fully dispersive mild-slope equation model for wave generation and propagation. This recreated model has the capability to simulate submarine landslides that detach into multiple rigid pieces as failure occurs. An ad-hoc formulation describing the combined space-time coherency of the landslide is presented. Monte Carlo simulations are employed, with an emphasis on the shoreward-traveling waves, to construct probability of exceedance curves for the maximum dimensionless wave height from which wave statistics can be extracted. As inputs to the model, eight dimensionless parameters are specified both deterministically in the form of parameter spaces and probabilistically with normal distributions. Based on a sensitivity analysis, the results of this study indicate that submarine landslides with large width to thickness ratios and coherent failure behavior are most effective in generating tsunamis. Failures modes involving numerous slide pieces that fail in a very compact fashion, however, were observed to induce bigger waves than more coherent landslides. Rapid weakening in tsunami generation potential for some of the parameter combinations suggests that the hazard posed by submarine landslide tsunamis is strongly dependent on source features and local conditions and is only of concern for landslides of substantial dimensions

A hybrid model for large scale simulation of unsteady nonlinear waves

A hybrid model for simulating rogue waves in random seas on a large time and space scale is proposed in this thesis. It is formed by combining the derived fifth order Enhanced Nonlinear Schrödinger Equation based on Fourier transform (ENLSE-5F), the fully nonlinear Enhanced Spectral Boundary Integral (ESBI) method and its simplified version. The numerical techniques and algorithm for coupling three models on time scale are provided. Using them, and the switch between the three models during the computation is triggered automatically according to wave nonlinearities. Numerical tests are carried out and the results indicate that this hybrid model could simulate rogue waves both accurately and efficiently. In some cases showed, the hybrid model is more than 10 times faster than just using the ESBI method