| Description |
1 online resource (118 pages) |
| Series |
Memoirs of the American Mathematical Society Ser. ; v. 253 |
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Memoirs of the American Mathematical Society Ser
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| Contents |
880-01 Cover; Title page; Chapter 1. Introduction; 1.1. Munk boundary layers; 1.1.1. State of the art; 1.1.2. Boundary layer degeneracies; 1.1.3. Stability of the stationary Munk equation; 1.2. Geometrical preliminaries; 1.2.1. Regularity and flatness assumptions; 1.2.2. Singularity lines; 1.2.3. Domains with islands; 1.2.4. Periodic domains and domains with corners; 1.3. Main approximation results; 1.3.1. General case; 1.3.2. Periodic and rectangle cases; 1.3.3. Outline of the paper; Chapter 2. Multiscale analysis; 2.1. Local coordinates and the boundary layer equation |
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880-01/(S 3.2.1. Traces of the East boundary layers3.2.2. Definition of the East corrector; 3.3. North and South boundary layers; 3.3.1. Definition of the initial boundary value problem; 3.3.2. Estimates for _{, }; 3.3.3. Extinction and truncation; 3.4. The interface layer; 3.4.1. The lifting term \psil; 3.4.2. The interior singular layer ̂{Σ}; 3.4.3. Connection with the West boundary; 3.5. Lifting the West boundary conditions; 3.6. Approximate solution in the periodic and rectangle case; 3.6.1. In the periodic case; 3.6.2. In the rectangle case; Chapter 4. Proof of convergence |
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2.2. East and West boundary layers2.2.1. The scaled equation; 2.2.2. Domain of validity; 2.3. North and South boundary layers; 2.3.1. The scaled equation; 2.3.2. Study of the boundary layer equation (2.11):; 2.3.3. Boundary conditions for ∈( ᵢ, ᵢ₊₁); 2.3.4. Connection with East and West boundary layers; 2.4. Discontinuity zones; 2.4.1. Lifting the discontinuity; 2.4.2. The interior singular layer; 2.5. The case of islands; 2.6. North and South periodic boundary layers; Chapter 3. Construction of the approximate solution; 3.1. The interior term; 3.2. Lifting the East boundary conditions |
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4.1. Remainders stemming from the interior term ̂{ }= ⁰_{ }+\psil4.1.1. Error terms due to the truncation _{\viscosite}.; 4.1.2. Error terms due to the lifting term \psil; 4.2. Remainders coming from the boundary terms; 4.2.1. Laplacian in curvilinear coordinates; 4.2.2. Error terms associated with North and South layers; 4.2.3. Error terms associated with East and West boundary layers; 4.2.4. Error terms associated with discontinuity layers; 4.3. Remainders in the periodic and rectangular cases; Chapter 5. Discussion: Physical relevance of the model; Acknowledgments; Appendix |
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Appendix A: The case of islands: derivation of the compatibility condition (1.15) and proof of Lemma 1.2.1Appendix B: Equivalents for the coordinates of boundary points near horizontal parts; Appendix C: Estimates on the coefficients and .; Appendix D: Proof of Lemma 3.4.3; Notations; Sizes of parameters and terms; Bibliography; Back Cover |
| Summary |
This paper is concerned with a complete asymptotic analysis as E \to 0 of the Munk equation \partial _x\psi -E \Delta ̂2 \psi = \tau in a domain \Omega \subset \mathbf R̂2, supplemented with boundary conditions for \psi and \partial _n \psi . This equation is a simple model for the circulation of currents in closed basins, the variables x and y being respectively the longitude and the latitude. A crude analysis shows that as E \to 0, the weak limit of \psi satisfies the so-called Sverdrup transport equation inside the domain, namely \partial _x \psi ̂0=\tau, while boundary layers appear in |
| Notes |
Print version record |
| Subject |
Boundary layer.
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Ocean currents -- Mathematical models
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Ocean circulation -- Mathematical models
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Boundary layer
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Ocean circulation -- Mathematical models
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Ocean currents -- Mathematical models
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| Form |
Electronic book
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| Author |
Saint-Raymond, Laure
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| ISBN |
9781470444075 |
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1470444070 |
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