Dissipative Boussinesq equations

The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated numerically.Comment: 40 pages, 15 figures, published in C. R. Mecanique 335 (2007) Other author's papers can be downloaded at http://www.cmla.ens-cachan.fr/~dutyk

The VOLNA code for the numerical modelling of tsunami waves: generation, propagation and inundation

A novel tool for tsunami wave modelling is presented. This tool has the potential of being used for operational purposes: indeed, the numerical code \VOLNA is able to handle the complete life-cycle of a tsunami (generation, propagation and run-up along the coast). The algorithm works on unstructured triangular meshes and thus can be run in arbitrary complex domains. This paper contains the detailed description of the finite volume scheme implemented in the code. The numerical treatment of the wet/dry transition is explained. This point is crucial for accurate run-up/run-down computations. Most existing tsunami codes use semi-empirical techniques at this stage, which are not always sufficient for tsunami hazard mitigation. Indeed the decision to evacuate inhabitants is based on inundation maps which are produced with this type of numerical tools. We present several realistic test cases that partially validate our algorithm. Comparisons with analytical solutions and experimental data are performed. Finally the main conclusions are outlined and the perspectives for future research presented.Comment: 47 pages, 27 figures. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

Linear theory of wave generation by a moving bottom

The computation of long wave propagation through the ocean obviously depends on the initial condition. When the waves are generated by a moving bottom, a traditional approach consists in translating the ``frozen'' sea bed deformation to the free surface and propagating it. The present study shows the differences between the classical approach (passive generation) and the active generation where the bottom motion is included. The analytical solutions presented here exhibit some of the drawbacks of passive generation. The linearized solutions seem to be sufficient to consider the generation of water waves by a moving bottom.Comment: 9 pages, 2 figure

The Force of a Tsunami on a Wave Energy Converter

With an increasing emphasis on renewable energy resources, wave power technology is fast becoming a realistic solution. However, the recent tsunami in Japan was a harsh reminder of the ferocity of the ocean. It is known that tsunamis are nearly undetectable in the open ocean but as the wave approaches the shore its energy is compressed creating large destructive waves. The question posed here is whether a nearshore wave energy converter (WEC) could withstand the force of an incoming tsunami. The analytical 3D model of Renzi & Dias (2012) developed within the framework of a linear theory and applied to an array of fixed plates is used. The time derivative of the velocity potential allows the hydrodynamic force to be calculated.Comment: 12 pages, 6 figures, 2 tables, 16 references. Paper presented at the ISOPE-2012 conference. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

Energy of tsunami waves generated by bottom motion

In the vast literature on tsunami research, few articles have been devoted to energy issues. A theoretical investigation on the energy of waves generated by bottom motion is performed here. We start with the full incompressible Euler equations in the presence of a free surface and derive both dispersive and non-dispersive shallow-water equations with an energy equation. It is shown that dispersive effects only appear at higher order in the energy budget. Then we solve the Cauchy-Poisson problem of tsunami generation for the linearized water wave equations. Exchanges between potential and kinetic energies are clearly revealed.Comment: 20 pages, 12 figures. Accepted to Proceedings of the Royal Society A. Other authors papers and supporting material can be downloaded at http://www.lama.univ-savoie.fr/~dutyk