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Mathematical Study of Degenerate Boundary Layers: A Large Scale Ocean Circulation Problem
 
Anne-Laure Dalibard Université Pierre et Marie Curie, Paris, France
Laure Saint-Raymond École Normale Supérieure, Paris, France
Mathematical Study of Degenerate Boundary Layers: A Large Scale Ocean Circulation Problem
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
Mathematical Study of Degenerate Boundary Layers: A Large Scale Ocean Circulation Problem
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Mathematical Study of Degenerate Boundary Layers: A Large Scale Ocean Circulation Problem
Anne-Laure Dalibard Université Pierre et Marie Curie, Paris, France
Laure Saint-Raymond École Normale Supérieure, Paris, France
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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2532018; 111 pp
    MSC: 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.

  • 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
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2532018; 111 pp
MSC: 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.

  • Chapters
  • 1. Introduction
  • 2. Multiscale analysis
  • 3. Construction of the approximate solution
  • 4. Proof of convergence
  • 5. Discussion: Physical relevance of the model
  • Appendix
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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