Introduction to PDEs and Waves for the Atmosphere and Ocean (Courant Lecture Notes)
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Written by a leading specialist in the area of atmosphere/ocean science (AOS), this book presents an excellent introduction to this important topic. 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 them with 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 AOS. It is excellent for supplementary course reading or independent study.
Introduction Some remarkable features of stratified flow Linear and nonlinear instability of stratified flows with strong stratification Rotating shallow water theory Linear and weakly nonlinear theory of dispersive waves with geophysical examples Simplified equations for the dynamics of strongly stratified flow The stratified quasi-geostrophic equations as a singular limit of the rotating Boussinesq equations Introduction to averaging over fast waves for geophysical flows Waves and PDEs for the equatorial atmosphere and ocean Bibliography.
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