Waves and Mean Flows

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Overview

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. This book 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. It can be used as a fundamental reference, a course text, or by geophysicists and physicists needing a first introduction. This second edition includes brand new material, including a section on Langmuir circulations and the Craik–Leibovich instability. The author has also added exercises to aid students' learning.

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Editorial Reviews

From the Publisher
Review of the first edition: 'Its approach is systematic, building surely and steadily from the simplest examples to the most far-reaching generalizations, and it should therefore suit graduate students and mature researchers alike. And on top of that, it's fun to read! The style is witty and occasionally quirky, but adds up to an almost miraculous combination of succinctness and explicitness.' M. E. Young, Journal of Fluid Mechanics

Review of the first edition: 'Bühler's well-organized textbook is excellent in all the most important ways. The author is well known in the field for applications of the GLM formulation to real-world problems, and his book will likely become the authoritative resource on the subject. Waves and Mean Flows presents its readers with a clearly written text that is comfortable to read. As a logically laid-out, internally consistent, and self-contained work, it will be useful both as a textbook and as a handy reference for researchers.' Steve K. Lamoreaux, Physics Today

Review of the first edition: 'For anyone wishing to work seriously with the GLM approach, Waves and Mean Flows is indispensable.' Physics Today

Review of the first edition: '… this text is, to my knowledge, the best existing source for a comprehensive introduction to the GLM theory. Many important concepts, such as the development of Lagrangian-mean divergence in divergence-free Eulerian flows, are explained with clarity, often through the use of elegant examples … Its intentionally provocative deviation from habitual Eulerian-mean thinking is certain to prove valuable and stimulating, and will no doubt have the desired long-term mean effect of raising the scientific community's conceptual center of gravity in this important field of inquiry.' Bulletin of the American Meteorological Society

Review of the first edition: 'The book is written in a very unpretentious, direct style. This book is an excellent investment for atmospheric and oceanic dynamicists and many environmental and mechanical engineers. Applied mathematicians who want to understand geophysical waves deeply and/or ray tracing will like this book, too.' SIAM Review

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Product Details

Meet the Author

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

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Table of Contents

Preface;
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; Bibliography; Index.

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