eBook ISBN:  9781470444075 
Product Code:  MEMO/253/1206.E 
List Price:  $78.00 
MAA Member Price:  $70.20 
AMS Member Price:  $46.80 
eBook ISBN:  9781470444075 
Product Code:  MEMO/253/1206.E 
List Price:  $78.00 
MAA Member Price:  $70.20 
AMS Member Price:  $46.80 

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 socalled Sverdrup transport equation inside the domain, namely \(\partial _x \psi ^0=\tau \), while boundary layers appear in the vicinity of the boundary.

Table of Contents

Chapters

1. Introduction

2. Multiscale analysis

3. Construction of the approximate solution

4. Proof of convergence

5. Discussion: Physical relevance of the model

Appendix


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 socalled Sverdrup transport equation inside the domain, namely \(\partial _x \psi ^0=\tau \), while boundary layers appear in the vicinity of the boundary.

Chapters

1. Introduction

2. Multiscale analysis

3. Construction of the approximate solution

4. Proof of convergence

5. Discussion: Physical relevance of the model

Appendix