Introduction to PDEs and Waves for the Atmosphere and Ocean

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Overview

The goals of these lecture notes, based on courses presented by the author at the Courant Institute of Mathematical Sciences, are to introduce mathematicians to the fascinating and important area of atmosphere/ocean science (AOS) and, conversely, to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community, ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied mathematics and geophysical flows in the style of modern applied mathematics, where rigorous mathematical analysis as well as asymptotic, qualitative, and numerical modeling all interact to ease the understanding of physical phenomena. Reading these lecture notes does not require a previous course in fluid dynamics, although a serious reader should supplement these notes with material such as additional information on geophysical flows, as suggested in the preface. The book is intended for graduate students and researchers working in interdisciplinary areas between mathematics and atmosphere/ocean science.

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Product Details

  • ISBN-13: 9780821829547
  • Publisher: American Mathematical Society
  • Publication date: 1/10/2003
  • Series: Courant Lecture Notes Series , #9
  • Edition description: New Edition
  • Pages: 234
  • Product dimensions: 6.90 (w) x 9.90 (h) x 0.50 (d)

Table of Contents

Preface
Ch. 1 Introduction 1
Ch. 2 Some Remarkable Features of Stratified Flow 9
Ch. 3 Linear and Nonlinear Instability of Stratified Flows with Strong Stratification 31
Ch. 4 Rotating Shallow Water Theory 49
Ch. 5 Linear and Weakly Nonlinear Theory of Dispersive Waves with Geophysical Examples 79
Ch. 6 Simplified Equations for the Dynamics of Strongly Stratified Flow 125
Ch. 7 The Stratified Quasi-Geostrophic Equations as a Singular Limit of the Rotating Boussinesq Equations 147
Ch. 8 Introduction to Averaging over Fast Waves for Geophysical Flows 171
Ch. 9 Waves and PDEs for the Equatorial Atmosphere and Ocean 199
Bibliography 233
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