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Interactions between waves and mean flows play a crucial role in understanding the long-term aspects of atmospheric and oceanographic modelling. Indeed, our ability to predict climate change hinges on our ability to model waves accurately.
Waves and Mean Flows gives a modern account of the nonlinear interactions between waves and mean flows such as shear flows and vortices. A detailed account of the theory of linear dispersive waves in moving media is followed by a thorough introduction to classical wave-mean interaction theory. The author then extends the scope of the classical theory and lifts its restriction to zonally symmetric mean flows.
Waves and Mean Flows is a fundamental reference for graduate students and researchers in fluid mechanics, and can be used as a text for advanced courses; it will also be appreciated by geophysicists and physicists who need an introduction to this important area in fundamental fluid dynamics and atmosphere-ocean science.
Part I. Fluid Dynamics and Waves
1. Elements of fluid dynamics
2. Linear waves
3. Geometric wave theory
4. Dispersive waves and ray tracing
Part II. Wave-Mean Interaction Theory
5. Zonally symmetric wave-mean interaction theory
6. Internal gravity waves
7. Shear flows
8. Three-dimensional rotating flow
9. Rossby waves and balanced dynamics
10. Lagrangian-mean theory
11. Zonally symmetric GLM theory
Part III. Waves and Vortices
12. A framework for local interactions
13. Wave-driven vortex dynamics on beaches
14. Wave refraction by vortices
Oliver Buhler is an Associate Professor in the Department of Mathematics at the Courant Institute of Mathematical Sciences, New York University.
"Buhler's well-organized textbook is excellent in all the most important ways [...] Waves and Mean Flows presents its readers with a clearly written text that is comfortable to read."
- Physics Today