For a scientific approach to extreme events Asymptotic analysis of typhoons and tsunami Daniela...

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

Kirogi

1000 500 500 1000x

1000

500

500

1000

q

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)

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 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)

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)

Neural Network (1/4)

Hugoniot-Maslov Hierarchy 1/15

Hugoniot-Maslov Hierarchy 2/15

Hugoniòt-Maslov Hierarchy 3/15

More phenomenology (1/4)

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

-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

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

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

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

For a scientific approach to extreme events Asymptotic analysis of typhoons and tsunami Daniela...

Documents

Transcript of For a scientific approach to extreme events Asymptotic analysis of typhoons and tsunami Daniela...