Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis.

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Presentation transcript:

Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis of the wave profiles near the fronts appearing in Tsunami problems

“Gaussian” source of Earthquake

Level curves of perturbation

Wave profiles at the front at time t at different angles

3D wave profile for elliptic source

“Modulated gaussian” source of Earthquake

Level curves of perturbation

Wave profiles at the front at time t at different angles

3D wave profile for elliptic source

The ridge near the source of Eathquake

Fronts at different times

The set of profiles

Simulations for Tyrrhenian Sea Relief data: National Oceanic and Atmospheric Administration (NOAA) National Geophysical Data Center (NGDC) ETOPO2 2-minute Global Relief

Rays for imaginary source at Stromboli: 38.8 N, 15.2 E

Amplitudes of wave at different points of the coast

3D wave profile

Density plot

DD7-29/05/07-01/06/07 Special session on tsunami and typhoons Scattering of tsunami on the beach S.Dobrokhotov Inst. Probl. of Mechanics R. Ac Sc. Moscow Petya Zhevandrov Escuela de Ciencias Fisico-Matematicas, Morelia, Mexico Brunello Tirozzi Department of Physics, Univ. “La Sapienza”, Rome

... Workshop on Extreme Events... Max Planck Institut for Complex System Dresden, 30 October-2 November 2006 Analysis of the tsunami event in Algeria 2003 B. Tirozzi (1),F. Raicich (2) (1) Department of Physics, University “La Sapienza”, Rome, Italy (2) CNR, Institute of Marine Sciences, Trieste, Italy

Valencia Barcelona Ibiza Earthquake data (USGS): t0: 18:44:19 GMT, 21 may 2003 USGS: epicenter 36.96°N, 3.63°E, M=6.9, hf=12 km Borerro: epicenter 36.90°N, 3.71°E, M=6.8, hf=10 km, strike=56°

Ellipsoidal deformation M = 6.9 h f = 12 km (Pelinovsky et al., 2001) a = 34 km b = 12 km b 56° a Coordinates: model gridpoints

(Dobrokhotov et al., 2006) a 1 = km -1 Gaussian*cosine deformation = 0 a 2 = km -1 b 1 = km -2 b 2 = km -2 = 56° Coordinates: model gridpoints

Linear theory of the scattering of localized waves on a beach of constant slope S. Dobrokhotov, Petya Zhevandrov, Brunello Tirozzi

Shape of perturbation

Amplitude of the waves at tsunami front

Average of the too fast oscillating WKB solution

Example: beach of costant slope

Momentum equation

Singular Lagrangian manifold

Dynamic on the lagrangian manifold

Dynamic on the phase space

Solutions before and after the scattering of the beach (1/2)

Solutions before and after the scattering of the beach (2/2)

Graphics 1

Graphics 2

Graphics 3

End