Keywords: Boussinesq equations, Serre´s equations, landslides,.

Water waves generated by landslides have been long menace in certain localities and the study of this phenomenon has been carried out at an accelerated rate in the last decades. Doubtless the phase of wave creation is very complex. We observe, at the impact, splash effect and the dissipation of energy, such as through turbulent dissipation at the plunge point, internal and external friction losses of the plunging mass (into the water), generation of shock waves, and deformation of the mass and of the bottom of the reservoir or lake. This very complex phenomenon is discussed in this paper by numerical and experimental approaches. In general, a model based on shallow water equations with shocks (Saint Venant's equations) has been developed by this author and others researches. It can reproduce the amplitude and the energy of the wave quite well, but because it consistenly generates a hydraulic jump, it is able to reproduce the profile, in the case of high relative thickness of slide, but in the case of small relative thickness it is unable to reproduce the amplitude of the wave. In this way, a numerical model based on Boussinesq equations (Serre's model) is used to describe water waves generated by local disturbance. Landslides in natural lakes or reservoirs of dams, avalanches, debris- flows, etc, can generate these sort of waves. Similar phenomenon, such as waves generated by the movement of ships in navigation channels can be also responsible by sliding of margins.

In order to validate the numerical model, experiments and numerical results are systematically compared. The experimental results are obtained from an experimental apparatus performed in the Hydraulic Laboratory of FEIS/UNESP.

The physical simulation representing the action of the solid mass in the water is done by block sliding on the ramp and plunging into wave canal. We observed that the features waves depend of block's geometry, its dynamic action inside of the liquid mass, slide distance in relation to the free surface and the initial depth of water. The analysis of incurred risks depends on of the good estimate of wave amplitude generated, because as larger the height of the wave, as larger will be the damages caused. So, the vertical acceleration has an important role in the free surface behavior.

This numerical model takes in account the vertical acceleration of the particles and considers higher orders derivate terms previously neglected by Boussinesq, so that in the generation zone, this model can support high relative amplitude of waves (neighborhoods of the breaking phenomenon)

A numerical model based on those equations was developed using a finite difference technique. The results obtained with the accomplished physical experiments are compatible to the numerical ones and the errors observed in amplitudes and profiles of waves are acceptable to the engineering point of view.

The mathematical model pointed up, even weakly nonlinear and dispersive, seems to reproduce well the amplitude and profile of experimental water waves.

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