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For a scientific approach to extreme events Asymptotic analysis of typhoons and tsunami Daniela Bianchi, Department of Physics, Univ. Of Rome “La Sapienza” Sergey Dobrokhotov, Institute of Problem of Mechanics, Moscow Academy of Sciences Fabio Raicich, ISMAR, CNR Trieste Sergiy Reutskiy, Ukrainian Academy of Science, Kharkov Brunello Tirozzi, Department of Physics, Univ. Of Rome “La Sapienza”

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Poleward heat transport

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Wind system for water covered Earth

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Main wind system (Northern summer)

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Main wind system (Southern summer)

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Cyclon and Anticyclon

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Cyclogenesis at mid latitudes

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Westerlies-Rossby wave

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Nanmadol

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Forecast without heat exchange

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Sonca

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Forecast without heat exchange

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Kirogi

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Real and computed trajectory with heat exchange

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Real and forecast trajectory

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Maslov decomposition (1/2) x is the difference among the running point and the typhoon center F is a function with the singularity in the origin of the square root type S is a quadratic function of the coordinates x with different eigenvalues f(x,t), g(x,t) are smooth functions Self-similarity and stability properties

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Maslov decomposition (2/2)

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Cauchy Riemann conditions and stability of perturbations

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Perturbed solutions of SW equations (1/3)

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Perturbed solutions of SW equations (2/3)

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Perturbed solutions of SW equations (3/3)

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Conserved structure of the solution (1/2)

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Conserved structure of the solution (2/2)

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Chi variable at each 0.25 degrees for the 00 of 18.09.06 Sanshan positions: 37.1 N, 132.4 E (developed) Yagi positions: 20.5 N, 158.6 E (beginning) 1 : Chi =0.1282 sec^(-1)

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Computation of the trajectory of the center of typhoons

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SW+temp. eq. (1/2)

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Sw+temp.eq (2/2)

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Lax Wendroff Method (1/4)

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Lax Wendroff method (2/4)

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Lax Wendroff method (3/4)

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Lax-Wendroff Method (4/4)

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Stability of the vortex

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Non stability of the vortex

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Boundary conditions (1/3)

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Boundary conditions (2/3)

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Boundary conditions (3/3)

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Neural Network (1/4)

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Neural Network (2/4)

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Neural Network (3/4)

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Neural Network (4/4)

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Hugoniot-Maslov Hierarchy 1/15

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Hugoniot-Maslov Hierarchy 2/15

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Hugoniòt-Maslov Hierarchy 3/15

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Hugoniòt-Maslov Hierarchy 4/15

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Hugoniòt-Maslov Hierarchy 5/15

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Hugoniòt-Maslov Hierarchy 6/15

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Hugoniòt-Maslov Hierarchy 7/15

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Hugoniòt-Maslov Hierarchy 8/15

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Hugoniòt-Maslov Hierarchy 9/15

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Hugoniòt-Maslov Hierarchy 10/15

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Hugoniòt-Maslov Hierarchy 11/15

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Hugoniòt-Maslov Hierarchy 12/15

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Hugoniòt-Maslov Hierarchy 13/15

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Hugoniòt-Maslov Hierarchy 14/15

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Hugoniòt-Maslov Hierarchy 15/15

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More phenomenology (1/4)

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More phenomenology (2/4)

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More phenomenology (3/4)

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More phenomenology (4/4)

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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

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“Gaussian” source of Earthquake

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Level curves of perturbation

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Wave profiles at the front at time t at different angles

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3D wave profile for elliptic source

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“Modulated gaussian” source of Earthquake

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Level curves of perturbation

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Wave profiles at the front at time t at different angles

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3D wave profile for elliptic source

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The ridge near the source of Eathquake

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Fronts at different times

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The set of profiles

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Simulations for Tyrrhenian Sea Relief data: National Oceanic and Atmospheric Administration (NOAA) National Geophysical Data Center (NGDC) ETOPO2 2-minute Global Relief http://www.ngdc.noaa.gov/mgg/gdas/gd_designagrid.html

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

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Amplitudes of wave at different points of the coast

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3D wave profile

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Density plot

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... Workshop on Extreme Events... Max Planck Institut for Complex System Dresden, 30 October-2 November 2006 Analysis of the tsunami event in Algeria 2003 S. Dobrokhotov (1), B. Tirozzi (2), P. Zhevandrov (3), F. Raicich (4) (1) Institute for Problems in Mechanics, RAS, Moscow, Russia (2) Department of Physics, University “La Sapienza”, Rome, Italy (3) Escuela de Ciencias Fisico-Matematicas, Morelia, Mich., Mexico (4) CNR, Institute of Marine Sciences, Trieste, Italy

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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°

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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

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(Dobrokhotov et al., 2006) a 1 = 1.2 10 -2 km -1 Gaussian*cosine deformation = 0 a 2 = 2.7 10 -2 km -1 b 1 = 0.5 10 -2 km -2 b 2 = 4.0 10 -2 km -2 = 56° Coordinates: model gridpoints

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Wave equation

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Average of fast oscillating solutions

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Amplitude of the waves at tsunami front

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

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

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Graphics 1

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Graphics 2

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Graphics 3

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