Introduction to PDEs and Waves for the Atmosphere and Ocean

Written by a leading specialist in the area of atmosphere/ocean science (AOS), the 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.

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