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

-5

-2.5

0

2.5

5-5

-2.5

0

2.5

5

00.250.5

0.751

-5

-2.5

0

2.5

5

Level curves of perturbation

-2-1

01

2

-4-2

024

Wave profiles at the front at time t at different angles

-4 -2 2 4

-0.5

0.5

1

1.5

3D wave profile for elliptic source

-20

-10

0

10

20-20

-10

0

10

20

-0.500.511.5

-20

-10

0

10

20

“Modulated gaussian” source of Earthquake

-5

-2.5

0

2.5

5-5

-2.5

0

2.5

5

-2

0

2

-5

-2.5

0

2.5

5

Level curves of perturbation

-2-1

01

2

-4-2

024

Wave profiles at the front at time t at different angles

-4 -2 2 4

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1

3D wave profile for elliptic source

-20

-10

0

10

20-20

-10

0

10

20

-2-1012

-20

-10

0

10

20

The ridge near the source of Eathquake

-5

0

5

-5

0

5

-3

-2

-1

0

-5

0

5-6 -4 -2 0 2 4 6

-6

-4

-2

0

2

4

6

Fronts at different times

The set of profiles

-20 -15 -10 -5 5 10 15 20

-20

-15

-10

-5

5

10

15

20

0.658889

1.48386

1.03988

0.0444183

1.03364

1.47197

0.658554

0.00228282

-20 -15 -10 -5 5 10 15 20

-20

-15

-10

-5

5

10

15

20

0.658889

1.48386

1.03988

0.0444183

1.03364

1.47197

0.658554

0.00228282

Simulations for Tyrrhenian Sea

-400 -200 0 200 400

-400

-200

0

200

400

-400 -200 0 200 400

-400

-200

0

200

400

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

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

50 100 150 200 250 300 350 400

-400

-350

-300

-250

-200

-150

-100

-50

Amplitudes of wave at different points of the coast

150 200 250 300 350 400 450

-350

-300

-250

-200

-150

-100

0.155356

0.0916952

0.118962

0.019779

0.00317829

0.09830570.0886875

0.306578

0.1297210.00840296

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 ZhevandrovEscuela de Ciencias Fisico-Matematicas, Morelia, Mexico

Brunello TirozziDepartment of Physics, Univ. “La Sapienza”, Rome

... Workshop on Extreme Events ...Max Planck Institut for Complex SystemDresden, 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

hf = 12 km

(Pelinovsky et al., 2001)

a = 34 km

b = 12 km

b56°

a

Coordinates: model gridpoints

(Dobrokhotov et al., 2006)

a1= 1.2 10-2 km-1

Gaussian*cosine deformation

= 0

a2 = 2.7 10-2 km-1

b1 = 0.5 10-2 km-2

b2 = 4.0 10-2 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