For a scientific approach to extreme events Asymptotic analysis of typhoons and tsunami Daniela Bianchi, Department of Physics, Univ. Of Rome “La Sapienza”

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Presentation transcript:

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”

Poleward heat transport

Wind system for water covered Earth

Main wind system (Northern summer)

Main wind system (Southern summer)

Cyclon and Anticyclon

Cyclogenesis at mid latitudes

Westerlies-Rossby wave

Nanmadol

Forecast without heat exchange

Sonca

Forecast without heat exchange

Kirogi

Real and computed trajectory with heat exchange

Real and forecast trajectory

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

Maslov decomposition (2/2)

Cauchy Riemann conditions and stability of perturbations

Perturbed solutions of SW equations (1/3)

Perturbed solutions of SW equations (2/3)

Perturbed solutions of SW equations (3/3)

Conserved structure of the solution (1/2)

Conserved structure of the solution (2/2)

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

Computation of the trajectory of the center of typhoons

SW+temp. eq. (1/2)

Sw+temp.eq (2/2)

Lax Wendroff Method (1/4)

Lax Wendroff method (2/4)

Lax Wendroff method (3/4)

Lax-Wendroff Method (4/4)

Stability of the vortex

Non stability of the vortex

Boundary conditions (1/3)

Boundary conditions (2/3)

Boundary conditions (3/3)

Neural Network (1/4)

Neural Network (2/4)

Neural Network (3/4)

Neural Network (4/4)

Hugoniot-Maslov Hierarchy 1/15

Hugoniot-Maslov Hierarchy 2/15

Hugoniòt-Maslov Hierarchy 3/15

Hugoniòt-Maslov Hierarchy 4/15

Hugoniòt-Maslov Hierarchy 5/15

Hugoniòt-Maslov Hierarchy 6/15

Hugoniòt-Maslov Hierarchy 7/15

Hugoniòt-Maslov Hierarchy 8/15

Hugoniòt-Maslov Hierarchy 9/15

Hugoniòt-Maslov Hierarchy 10/15

Hugoniòt-Maslov Hierarchy 11/15

Hugoniòt-Maslov Hierarchy 12/15

Hugoniòt-Maslov Hierarchy 13/15

Hugoniòt-Maslov Hierarchy 14/15

Hugoniòt-Maslov Hierarchy 15/15

More phenomenology (1/4)

More phenomenology (2/4)

More phenomenology (3/4)

More phenomenology (4/4)

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

... 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

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

Wave equation

Average of fast oscillating solutions

Amplitude of the waves at tsunami front

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