Turbulence, Coherent Structures, Dynamical Systems and Symmetry

Turbulence pervades our world, from weather patterns to the air entering our lungs. This book describes methods that reveal its structures and dynamics. Building on the existence of coherent structures – recurrent patterns – in turbulent flows, it describes mathematical methods that reduce the governing (Navier–Stokes) equations to simpler forms that can be understood more easily. This second edition contains a new chapter on the balanced proper orthogonal decomposition: a method derived from control theory that is especially useful for flows equipped with sensors and actuators. It also reviews relevant work carried out since 1995. The book is ideal for engineering, physical science and mathematics researchers working in fluid dynamics and other areas in which coherent patterns emerge.

Spis treści:
Part I. Turbulence
1. Introduction
2. Coherent structures
3. Proper orthogonal decomposition
4. Galerkin projection
5. Balanced proper orthogonal decomposition
Part II. Dynamical Systems
6. Qualitative theory
7. Symmetry
8. One-dimensional turbulence
9. Randomly-perturbed systems
Part III. The Boundary Layer
10. Low-dimensional models
11. Behaviour of the models
Part IV. Other Applications and Related Work
12. Some other fluid problems
13. Review, prospects for rigor
Index.