eBook ISBN: | 978-1-4704-4407-5 |
Product Code: | MEMO/253/1206.E |
List Price: | $78.00 |
MAA Member Price: | $70.20 |
AMS Member Price: | $46.80 |
eBook ISBN: | 978-1-4704-4407-5 |
Product Code: | MEMO/253/1206.E |
List Price: | $78.00 |
MAA Member Price: | $70.20 |
AMS Member Price: | $46.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 253; 2018; 111 ppMSC: Primary 35
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 \(\Omega \subset \mathbf R^2\), 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 the vicinity of the boundary.
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Table of Contents
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Chapters
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1. Introduction
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2. Multiscale analysis
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3. Construction of the approximate solution
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4. Proof of convergence
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5. Discussion: Physical relevance of the model
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Appendix
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Additional Material
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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 \(\Omega \subset \mathbf R^2\), 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 the vicinity of the boundary.
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Chapters
-
1. Introduction
-
2. Multiscale analysis
-
3. Construction of the approximate solution
-
4. Proof of convergence
-
5. Discussion: Physical relevance of the model
-
Appendix