For nearly a century now, hydrodynamic stability has been recognized as one of the central problems of fluid mechanics. It is concerned with when and how laminar flows break down, their subsequent development, and their eventual transition to turbulence. It has many applications in engineering, in meteorology and oceanography, and in astrophysics and geophysics. Some of these applications are mentioned, but the book is written from the point of view intrinsic to fluid mechanics and applied mathematics. Thus, although we have emphasized the analytical aspects of the theory, we have also tried, wherever possible, to relate the theory to experimental and numerical results.

Our aim in writing this book has been twofold. Firstly, in Chapters 1–4, to describe the fundamental ideas, methods, and results in three major areas of the subject: thermal convection, rotating and curved flows, and parallel shear flows. Secondly, to provide an introduction to some aspects of the subject which are of current research interest. These include some of the more recent developments in the asymptotic theory of the Orr–Sommerfeld equation in Chapter 5, some applications of the linear stability theory in Chapter 6 and finally, in Chapter 7, a discussion of some of the fundamental ideas involved in current work on the nonlinear theory of hydrodynamic stability.

Each chapter ends with a number of problems which often extend or supplement the main text as well as provide exercises to help the reader understand the topics.