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Documents  Critères de recherche : "Water waves" | enregistrements trouvés : 15

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- 235 p.
ISBN 978-0-8218-0510-7

Contemporary mathematics , 0200

Localisation : Collection 1er étage

Benjamin # Brooke # Kharif # chaos # flux cylindrique en rotation # forme normale de Birkhoff # instabilité modulationnelle # instabilité spatiale # intégrabilité asymptotique # intéraction d'onde solitaire # modulation d'onde aquatique non linéaire faiblement # montée rapide # onde aquatique permanente hamiltonienne # onde de gravité capillaire quasi-périodique spatialement # onde de surface d'eau # onde solitaire KP généralisée # phènomène de glissement vers le bas en fréquence # radiation # scission soliton # simulation numérique de solution singulière # stabilité asymptotique # système dispersif conservatif # équation de Benjamin-Ono forcée # équation de Burgers généralisée # équation de Kadomtsev-Petviashvili # équation de Korteweg-De Vries # état lié non linéaire # évolution non linéaire Benjamin # Brooke # Kharif # chaos # flux cylindrique en rotation # forme normale de Birkhoff # instabilité modulationnelle # instabilité spatiale # intégrabilité asymptotique # intéraction d'onde solitaire # modulation d'onde aquatique non linéaire faiblement # montée rapide # onde aquatique permanente hamiltonienne # onde de gravité capillaire quasi-périodique spatialement # onde de surface d'eau # onde solitaire KP généralisée # phènomène de ...

35Q51 ; 35Q53 ; 76B15 ; 76B25

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- xiv; 283 p.
ISBN 978-1-107-56556-2

London mathematical society lecture note series , 0426

Localisation : Collection 1er étage

théorie du mouvement ondulatoire # vague # mécanique des fluides

76-06 ; 76B15 ; 76B20 ; 35Q35 ; 00B25

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Special events;Lagrange Days;History of Mathematics;Mathematical Physics

Lagrange - 19th century - water waves

01A55 ; 76B15

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Partial Differential Equations;Mathematical Physics

A good understanding of waves in shallow water, typically in coastal regions, is important for several environmental and societal issues: submersion risks, protection of harbors, erosion, offshore structures, wave energies, etc. The goal of this serie of lectures is to show how efficient asymptotic models can be derived from the full fluid equations (Navier-Stokes and Euler) and to point out several modelling, numerical and mathematical challenges that one still has to understand in order to describe correctly and efficiently such complex phenomena as wave breaking, overtopping, wave-structures interactions, etc.

I Derivation of several shallow water models

We will show how to derive several shallow water models (nonlinear shallow water equations, Boussinesq and Serre-Green-Naghdi systems) from the free surface Euler equations. We will consider first the case of an idealized configuration where no breaking waves are involved, where the water height does not vanish (no beach!), and where the flow is irrotational - this is the only configuration for which a rigorous justification of the asymptotic models can be justified.

II Brief analysis of these models.

We will briefly comment the mathematical structure of these equations, with a particular focus on the properties that are of interest for their numerical implementation. We will also discuss how these models behave in when the water height vanishes, since they are typically used in such configurations (see the lecture by P. Bonneton).

III Vorticity and turbulent effects

We will propose a generalization of the derivation of the main shallow water models in the presence of vorticity, and show that the standard irrotational shallow water models must be coupled with an equation for a ”turbulent” tensor. We will also make the link with a modelling of wave breaking proposed by Gavrilyuk and Richard in which wave breaking is taken into account as a source term in this additional equation.

IV Floating objects.

This last section will be devoted to the description of a new approach to describe the interaction of waves in shallow water with floating objects, which leads to several interesting mathematical and numerical issues.
A good understanding of waves in shallow water, typically in coastal regions, is important for several environmental and societal issues: submersion risks, protection of harbors, erosion, offshore structures, wave energies, etc. The goal of this serie of lectures is to show how efficient asymptotic models can be derived from the full fluid equations (Navier-Stokes and Euler) and to point out several modelling, numerical and mathematical ...

35Q86 ; 86A05 ; 35-XX

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Partial Differential Equations;Mathematical Physics

A good understanding of waves in shallow water, typically in coastal regions, is important for several environmental and societal issues: submersion risks, protection of harbors, erosion, offshore structures, wave energies, etc.

The goal of this serie of lectures is to show how efficient asymptotic models can be derived from the full fluid equations (Navier-Stokes and Euler) and to point out several modelling, numerical and mathematical challenges that one still has to understand in order to describe correctly and efficiently such complex phenomena as wave breaking, overtopping, wave-structures interactions, etc.

I Derivation of several shallow water models

We will show how to derive several shallow water models (nonlinear shallow water equations, Boussinesq and Serre-Green-Naghdi systems) from the free surface Euler equations. We will consider first the case of an idealized configuration where no breaking waves are involved, where the water height does not vanish (no beach!), and where the flow is irrotational - this is the only configuration for which a rigorous justification of the asymptotic models can be justified.

II Brief analysis of these models.

We will briefly comment the mathematical structure of these equations, with a particular focus on the properties that are of interest for their numerical implementation. We will also discuss how these models behave in when the water height vanishes, since they are typically used in such configurations (see the lecture by P. Bonneton).

III Vorticity and turbulent effects.

We will propose a generalization of the derivation of the main shallow water models in the presence of vorticity, and show that the standard irrotational shallow water models must be coupled with an equation for a ”turbulent” tensor. We will also make the link with a modelling of wave breaking proposed by Gavrilyuk and Richard in which wave breaking is taken into account as a source term in this additional equation.

IV Floating objects.

This last section will be devoted to the description of a new approach to describe the interaction of waves in shallow water with floating objects, which leads to several interesting mathematical and numerical issues.
A good understanding of waves in shallow water, typically in coastal regions, is important for several environmental and societal issues: submersion risks, protection of harbors, erosion, offshore structures, wave energies, etc.

The goal of this serie of lectures is to show how efficient asymptotic models can be derived from the full fluid equations (Navier-Stokes and Euler) and to point out several modelling, numerical and mathematical ...

35Q86 ; 86A05 ; 35-XX

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Partial Differential Equations;Mathematical Physics

A good understanding of waves in shallow water, typically in coastal regions, is important for several environmental and societal issues: submersion risks, protection of harbors, erosion, offshore structures, wave energies, etc.

The goal of this serie of lectures is to show how efficient asymptotic models can be derived from the full fluid equations (Navier-Stokes and Euler) and to point out several modelling, numerical and mathematical challenges that one still has to understand in order to describe correctly and efficiently such complex phenomena as wave breaking, overtopping, wave-structures interactions, etc.

I Derivation of several shallow water models

We will show how to derive several shallow water models (nonlinear shallow water equations, Boussinesq and Serre-Green-Naghdi systems) from the free surface Euler equations. We will consider first the case of an idealized configuration where no breaking waves are involved, where the water height does not vanish (no beach!), and where the flow is irrotational - this is the only configuration for which a rigorous justification of the asymptotic models can be justified.

II Brief analysis of these models.

We will briefly comment the mathematical structure of these equations, with a particular focus on the properties that are of interest for their numerical implementation. We will also discuss how these models behave in when the water height vanishes, since they are typically used in such configurations (see the lecture by P. Bonneton).

III Vorticity and turbulent effects.

We will propose a generalization of the derivation of the main shallow water models in the presence of vorticity, and show that the standard irrotational shallow water models must be coupled with an equation for a ”turbulent” tensor. We will also make the link with a modelling of wave breaking proposed by Gavrilyuk and Richard in which wave breaking is taken into account as a source term in this additional equation.

IV Floating objects.

This last section will be devoted to the description of a new approach to describe the interaction of waves in shallow water with floating objects, which leads to several interesting mathematical and numerical issues.
A good understanding of waves in shallow water, typically in coastal regions, is important for several environmental and societal issues: submersion risks, protection of harbors, erosion, offshore structures, wave energies, etc.

The goal of this serie of lectures is to show how efficient asymptotic models can be derived from the full fluid equations (Navier-Stokes and Euler) and to point out several modelling, numerical and mathematical ...

35Q86 ; 86A05 ; 35-XX

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- 567 p.
ISBN 978-0-471-57034-9

Wiley classis library

Localisation : Ouvrage RdC (STOK)

courant # écoulement # flux # hydrodynamique # hydrolique mathématique # mécanique des fluides

76B15 ; 76Bxx ; 76D33 ; 76Exx ; 76Q05

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- v; 123 p.
ISBN 978-1-4704-3103-7

Memoirs of the American Mathematical Society , 1227

Localisation : Collection 1er étage

vague irrotationnelle # tension superficielle # estimation d'énergie # analyse dispersive # singularité # résonance temporelle # opérateur de Dirichlet-Neumann en dimension 2

76B15 ; 35Q35 ; 35Q31 ; 35R35

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- 567 p.

Pure and applied mathematics , 0004

Localisation : Ouvrage RdC (STOK)

onde de l'eau # physique mathématique # équation aux dérivées partielles

76B15 ; 76B20 ; 76Bxx ; 76C10 ; 76D33

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- 544 p.
ISBN 978-0-12-208437-9

diffraction non linéaire d'onde aquatique # fluide non visqueux # instabilité non linéaire d'onde dispersives # mouvement d'onde transitoire # onde de bas fond0 non linéaire # onde de bateau # onde de surface sur l'eau # onde dispersive non linéaire # ondes aquatiques non linéaires # résistance d'onde # soliton # équation de mouvement de fluide non visqueux ou visqueux

76Axx ; 76Bxx

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- vii; 128 p.
ISBN 978-0-8218-4382-6

Memoirs of the american mathematical society , 0940

Localisation : Collection 1er étage

onde # flot multiphase # opérateur pseudo-différentiel # problème de valeures aux limites # théorie de la bifurcation # petit diviseur

76B15 ; 47J15 ; 35S15 ; 76B07

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- xx; 321 p.
ISBN 978-0-8218-9470-5

Mathematical surveys and monographs , 0188

Localisation : Collection 1er étage

hydrodynamique # équation de propagation # modélisation

76B15 ; 35Q53 ; 35Q55 ; 35J05 ; 35J25 ; 35-02

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- viii; 241 p.
ISBN 978-2-85629-821-3

Astérisque , 0374

Localisation : Périodique 1er étage

équation d'Euler à surface libre # méthode de formes normales # calcul paradifférentiel # champ de Klainerman

35B40 ; 35S50 ; 35Q35

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- v; 108 p.
ISBN 978-1-4704-3203-4

Memoirs of the American Mathematical Society , 1229

Localisation : Collection 1er étage

onde d'eau # estimation de Strichartz # calcul paradifférentiel

35Q35 ; 35S50 ; 35S15 ; 76B15

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- v; 171 p.
ISBN 978-1-4704-4069-5

Memoirs of the American Mathematical Society , 1273

Localisation : Collection 1er étage

KAM pour les EDP # onde d'eau # solution quasi-périodique # onde stationnaire

76B15 ; 37K55 ; 76D45 ; 37K50 ; 35S05

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