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.
"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
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
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Oliver Buhler is an Associate Professor in the Department of Mathematics at the Courant Institute of Mathematical Sciences, New York University.