Politecnico di Torino
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Politecnico di Torino
Anno Accademico 2007/08
01LEPKM
Onde lineari e non lineari
Dottorato di ricerca in Ingegneria Per La Gestione Delle Acque E Del Territorio - Torino
Docente Qualifica Settore Lez Es Lab Tut Anni incarico
Ambrosi Davide Carlo   O2 MAT/07 25 0 0 0 2
SSD CFU Attivita' formative Ambiti disciplinari
*** N/A ***    
Obiettivi dell'insegnamento
FinalitÓ del corso:
Aim of the course is to provide PhD students with the fundamental mathematical tools that allow to analyze wave propagation phenomena in classical physics, with an emphasis on environmental applications and the nonlinear non dispersive regime as a final aim. Applications will involve free surface flow in fluid dynamics, with examples related to both hydraulics (river flow) and oceanography (ocean waves) and geophysics (elastic internal and surface waves).
Programma
Programma del corso:
1. Basic elements of linear theory: propagation and dispersion, Fourier transform, spectrum, phase velocity and group velocity.
2. Progressive elastic waves in a continuous medium: longitudinal waves, transversal waves, Rayleigh waves.
3. Free surface flow: characteristic spatial and temporal scale lenghts and corresponding regimes, non-dimensional numbers.
4. Linear waves: dispersion relationship, deep water and shallow water limits. Tsunami.
5. Nonlinear nondispersive waves: shallow water equations. River flow: Riemann invariants, celerity of a flood wave.
6. Nonlinear dispersive waves: Korteweg de Vries equation, Boussinesq equation, solitons and cnoidal waves.
7. Asymptotic expansions, secular terms, uniform convergence. Multiscale analysis, nonlinear Schroedinger equation. Stability analysis for partial differential equarions, Benjamin-Feir instability.
Note

The course is thought to be activated on a two-years basis.
Orario delle lezioni
Statistiche superamento esami

Programma provvisorio per l'A.A.2007/08
Indietro



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