Introduction to Hydrodynamic Stability

Introduces instability of flows and their transition to turbulence. Suitable for a graduate course.

P. G. Drazin (Author)

9780521009652, Cambridge University Press

Paperback, published 9 September 2002

278 pages, 78 b/w illus.
22.5 x 15.1 x 1.4 cm, 0.38 kg

'Without either undue oversimplification or over-sophistication the author manages to present the fundamentals of hydrodynamic stability in a very lucid way. The exercises constitute a part of particular value. With their many comments and further thoughts they amount to much more than just to exercises in the plain meaning of the word.' Internationale Mathematische Nachrichten

Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.

1. General introduction
2. Introduction to steady flows, their instability and bifurcations
3. Kelvin–Helmholtz instability
4. Capillary instability of a jet
5. Development of instabilities in time and space
6. Rayleigh–Bénard convection
7. Centrifugal instability
8. Stability of parallel flows
9. Routes to chaos and turbulence
10. Case studies in transition to turbulence
References
Index.

Subject Areas: Fluid mechanics [PHDF]