489 research outputs found
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
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