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

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Presentation transcript:

For a scientific approach to extreme events Asymptotic analysis of typhoons 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)

CR conditions at the onset (1/2)

CR conditions at the onset (2/2)

CR conditions during the cyclon (1/2)

CR conditions during the cyclon (2/2)

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)

End