Instability in Geophysical Flows

William D. Smyth; Jeffrey R. Carpenter

doi:10.1017/9781108640084

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William D. Smyth, Oregon State University, Jeffrey R. Carpenter, Helmholtz-Zentrum Geesthacht

Publisher:: Cambridge University Press
Online publication date:: April 2019
Print publication year:: 2019
Online ISBN:: 9781108640084
DOI:: https://doi.org/10.1017/9781108640084
Creative Commons:: This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY-NC-ND 4.0 https://creativecommons.org/creativelicenses

Subjects:: Mathematics, Earth and Environmental Sciences, Fluid Dynamics and Solid Mechanics, Oceanography and Marine Science

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Instabilities are present in all natural fluids from rivers to atmospheres. This book considers the physical processes that generate instability. Part I describes the normal mode instabilities most important in geophysical applications, including convection, shear instability and baroclinic instability. Classical analytical approaches are covered, while also emphasising numerical methods, mechanisms such as internal wave resonance, and simple `rules of thumb' that permit assessment of instability quickly and intuitively. Part II introduces the cutting edge: nonmodal instabilities, the relationship between instability and turbulence, self-organised criticality, and advanced numerical techniques. Featuring numerous exercises and projects, the book is ideal for advanced students and researchers wishing to understand flow instability and apply it to their own research. It can be used to teach courses in oceanography, atmospheric science, coastal engineering, applied mathematics and environmental science. Exercise solutions and MATLAB® examples are provided online. Also available as Open Access on Cambridge Core.

'Written with impressive clarity, this new textbook covers all the key types of geophysical instability and provides a window to more advanced topics such as transient optimal growth and transition to turbulence. In addition to presenting the mathematical fundamentals the authors present satisfying physical explanations for the complex mechanisms, while throughout the text (and homework exercises) numerical methods and simple codes are used to familiarise students with this important tool for simulating instability mechanisms numerically. For all these reasons it is truly an outstanding textbook - for class teaching or self-study. I will use it myself to create a new graduate course!'

Eyal Heifetz - Tel Aviv University

‘… large number of analytical and numerical exercises, make the book suitable for use in teaching a graduate or upper-level undergraduate course on the subject of geophysical ﬂuid dynamics. The material covered would be helpful both to atmospheric science students and researchers who wish to understand the mathematical theory and numerical simulation techniques and to applied mathematics students and researchers who wish to learn more about the geophysical processes and the mechanisms that lead to the instabilities.’

Lucy J. Campbell Source: Mathematical Reviews Clippings

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Instability in Geophysical Flows

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Preface
pp ix-x

Acknowledgments
pp xi-xii

Part I - Normal Mode Instabilities
pp 1-2

1 - Preliminaries
pp 3-23

2 - Convective Instability
pp 24-52

3 - Instabilities of a Parallel Shear Flow
pp 53-106

4 - Parallel Shear Flow: the Effects of Stratification
pp 107-136

5 - Parallel Shear Flow: the Effects of Viscosity
pp 137-152

6 - Synthesis: Viscous, Diffusive, Inhomogeneous, Parallel Shear Flow
pp 153-173

7 - Nonparallel Flow: Instabilities of a Cylindrical Vortex
pp 174-194

8 - Instability in a Rotating Environment
pp 195-221

9 - Convective Instability in Complex Fluids
pp 222-241

10 - Summary
pp 242-244

Part II - The View Ahead
pp 245-246

11 - Beyond Normal Modes
pp 247-261

12 - Instability and Turbulence
pp 262-272

13 - Refining the Numerical Methods
pp 273-286

Appendix A - Homework Exercises
pp 287-306

Appendix B - Projects
pp 307-316

References
pp 317-322

Index
pp 323-328

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Instability in Geophysical Flows

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