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Documents  35Q86 | enregistrements trouvés : 20

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Multi angle  Nearshore hydrodynamics - Lecture 1
Bonneton, Philippe (Auteur de la Conférence) | CIRM (Editeur )

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Multi angle  Nearshore hydrodynamics - Lecture 2
Bonneton, Philippe (Auteur de la Conférence) | CIRM (Editeur )

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Multi angle  Nearshore hydrodynamics - Lecture 3
Bonneton, Philippe (Auteur de la Conférence) | CIRM (Editeur )

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Multi angle  Scales in geophysical flows - Lecture 1
Klein, Rupert (Auteur de la Conférence) | CIRM (Editeur )

Earth’s atmosphere hosts a rich spectrum of phenomena that involve interactions of a variety of processes across many length and time scales. A systematic approach to analyzing these scale dependent processes is a core task of theoretical meteorology and a prerequi- site to constructing reliable computational models for weather forecasting and climate simulation.

Lecture I The fundamental tools of similarity theory and formal single scale asymptotics will allow us to systematize the large zoo of scale-dependent model equations that one finds in modern textbooks of theoretical meteorology.

Lecture II The meteorological analogue of the incompressible flow equations are the ”anelastic” and ”pseudo-incompressible” models. Here we will learn how the presence of internal gravity waves in the atmosphere implies an asymptotic three-scale problem that renders the formal derivation and justification of these models much more intricate than the classical low Mach number derivation of the incompressible flow equations.

Lecture III The mechanisms by which tropical storms develop into hurricanes and typhoons are still under intense debate despite decades of research. A recent theory for the dynamics of strongly tilted atmospheric vortices will show how asymptotic methods help structuring this scientific debate, and how they offer new angles of scientific attack on the problem.

Lecture * If time permits, I will also summarize some ramifications of the scaling regimes and scaling theories considered in Lectures I-III on the construction of reliable computational methods.
Earth’s atmosphere hosts a rich spectrum of phenomena that involve interactions of a variety of processes across many length and time scales. A systematic approach to analyzing these scale dependent processes is a core task of theoretical meteorology and a prerequi- site to constructing reliable computational models for weather forecasting and climate simulation.

Lecture I The fundamental tools of similarity theory and formal single scale ...

35Q86 ; 35Qxx ; 86A35

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Earth’s atmosphere hosts a rich spectrum of phenomena that involve interactions of a variety of processes across many length and time scales. A systematic approach to analyzing these scale dependent processes is a core task of theoretical meteorology and a prerequi- site to constructing reliable computational models for weather forecasting and climate simulation.

Lecture I The fundamental tools of similarity theory and formal single scale asymptotics will allow us to systematize the large zoo of scale-dependent model equations that one finds in modern textbooks of theoretical meteorology.

Lecture II The meteorological analogue of the incompressible flow equations are the ”anelastic” and ”pseudo-incompressible” models. Here we will learn how the presence of internal gravity waves in the atmosphere implies an asymptotic three-scale problem that renders the formal derivation and justification of these models much more intricate than the classical low Mach number derivation of the incompressible flow equations.

Lecture III The mechanisms by which tropical storms develop into hurricanes and typhoons are still under intense debate despite decades of research. A recent theory for the dynamics of strongly tilted atmospheric vortices will show how asymptotic methods help structuring this scientific debate, and how they offer new angles of scientific attack on the problem.

Lecture * If time permits, I will also summarize some ramifications of the scaling regimes and scaling theories considered in Lectures I-III on the construction of reliable computational methods.
Earth’s atmosphere hosts a rich spectrum of phenomena that involve interactions of a variety of processes across many length and time scales. A systematic approach to analyzing these scale dependent processes is a core task of theoretical meteorology and a prerequi- site to constructing reliable computational models for weather forecasting and climate simulation.

Lecture I The fundamental tools of similarity theory and formal single scale ...

35Q86 ; 35Qxx ; 86A35

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Earth’s atmosphere hosts a rich spectrum of phenomena that involve interactions of a variety of processes across many length and time scales. A systematic approach to analyzing these scale dependent processes is a core task of theoretical meteorology and a prerequi- site to constructing reliable computational models for weather forecasting and climate simulation.

Lecture I The fundamental tools of similarity theory and formal single scale asymptotics will allow us to systematize the large zoo of scale-dependent model equations that one finds in modern textbooks of theoretical meteorology.

Lecture II The meteorological analogue of the incompressible flow equations are the ”anelastic” and ”pseudo-incompressible” models. Here we will learn how the presence of internal gravity waves in the atmosphere implies an asymptotic three-scale problem that renders the formal derivation and justification of these models much more intricate than the classical low Mach number derivation of the incompressible flow equations.

Lecture III The mechanisms by which tropical storms develop into hurricanes and typhoons are still under intense debate despite decades of research. A recent theory for the dynamics of strongly tilted atmospheric vortices will show how asymptotic methods help structuring this scientific debate, and how they offer new angles of scientific attack on the problem.

Lecture * If time permits, I will also summarize some ramifications of the scaling regimes and scaling theories considered in Lectures I-III on the construction of reliable computational methods.
Earth’s atmosphere hosts a rich spectrum of phenomena that involve interactions of a variety of processes across many length and time scales. A systematic approach to analyzing these scale dependent processes is a core task of theoretical meteorology and a prerequi- site to constructing reliable computational models for weather forecasting and climate simulation.

Lecture I The fundamental tools of similarity theory and formal single scale ...

35Q86 ; 35Qxx ; 86A35

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Multi angle  Modelling shallow water waves - Lecture 1
Lannes, David (Auteur de la Conférence) | CIRM (Editeur )

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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Multi angle  Modelling shallow water waves - Lecture 2
Lannes, David (Auteur de la Conférence) | CIRM (Editeur )

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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Multi angle  Modelling shallow water waves - Lecture 3
Lannes, David (Auteur de la Conférence) | CIRM (Editeur )

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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In these lectures, we will focus on the analysis of oceanographic models. These models involve several small parameters: Mach number, Froude number, Rossby number... We will present a hierarchy of models, and explain how they can formally be derived from one another. We will also present different mathematical tools to address the asymptotic analysis of these models (filtering methods, boundary layer techniques).

86A05 ; 34E13 ; 35Q30 ; 35Q86 ; 35Jxx

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In these lectures, we will focus on the analysis of oceanographic models. These models involve several small parameters: Mach number, Froude number, Rossby number... We will present a hierarchy of models, and explain how they can formally be derived from one another. We will also present different mathematical tools to address the asymptotic analysis of these models (filtering methods, boundary layer techniques).

86A05 ; 34E13 ; 35Q30 ; 35Q86 ; 35Jxx

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In these lectures, we will focus on the analysis of oceanographic models. These models involve several small parameters: Mach number, Froude number, Rossby number... We will present a hierarchy of models, and explain how they can formally be derived from one another. We will also present different mathematical tools to address the asymptotic analysis of these models (filtering methods, boundary layer techniques).

86A05 ; 34E13 ; 35Q30 ; 35Q86 ; 35Jxx

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In this talk, I will present the global solvability of the primitive equations for the atmosphere coupled to moisture dynamics with phase changes for warm clouds, where water is present in the form of water vapor and in the liquid state as cloud water and rain water. This moisture model, which has been used by Klein-Majda in [1] and corresponds to a basic form of the bulk microphysics closure in the spirit of Kessler [2] and Grabowski-Smolarkiewicz [3], contains closures for the phase changes condensation and evaporation, as well as the processes of autoconversion of cloud water into rainwater and the collection of cloud water by the falling rain droplets. The moisture balances are strongly coupled to the thermodynamic equation via the latent heat associated to the phase changes. The global well-posedness was proved by combining the technique used in Hittmeir-Klein-Li-Titi [4], where global well-posedness was established for the pure moisture system for given velocity, and the ideas of Cao-Titi [5], who succeeded in proving the global solvability of the primitive equations without coupling to the moisture.
In this talk, I will present the global solvability of the primitive equations for the atmosphere coupled to moisture dynamics with phase changes for warm clouds, where water is present in the form of water vapor and in the liquid state as cloud water and rain water. This moisture model, which has been used by Klein-Majda in [1] and corresponds to a basic form of the bulk microphysics closure in the spirit of Kessler [2] and Grabowski-S...

35A01 ; 35B45 ; 35D35 ; 35M86 ; 35Q30 ; 35Q35 ; 35Q86 ; 76D03 ; 76D09

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One of the main characteristics of infinite-dimensional dissipative evolution equations, such as the Navier-Stokes equations and reaction-diffusion systems, is that their long-time dynamics is determined by finitely many parameters - finite number of determining modes, nodes, volume elements and other determining interpolants. In this talk I will show how to explore this finite-dimensional feature of the long-time behavior of infinite-dimensional dissipative systems to design finite-dimensional feedback control for stabilizing their solutions. Notably, it is observed that this very same approach can be implemented for designing data assimilation algorithms of weather prediction based on discrete measurements. In addition, I will also show that the long-time dynamics of the Navier-Stokes equations can be imbedded in an infinite-dimensional dynamical system that is induced by an ordinary differential equations, named determining form, which is governed by a globally Lipschitz vector field. Remarkably, as a result of this machinery I will eventually show that the global dynamics of the Navier-Stokes equations is being determining by only one parameter that is governed by an ODE. The Navier-Stokes equations are used as an illustrative example, and all the above mentioned results equally hold to other dissipative evolution PDEs, in particular to various dissipative reaction-diffusion systems and geophysical models.
One of the main characteristics of infinite-dimensional dissipative evolution equations, such as the Navier-Stokes equations and reaction-diffusion systems, is that their long-time dynamics is determined by finitely many parameters - finite number of determining modes, nodes, volume elements and other determining interpolants. In this talk I will show how to explore this finite-dimensional feature of the long-time behavior of infinite-d...

35Q30 ; 35Q86

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