In this chapter the text begins with an informal introduction to the concept of stability and the nature of instability of a particular flow as a prototype – the flow along a pipe. The prototype illustrates the importance of instability as a prelude to transition to turbulence. Finally, the chief methods of studying instability of flows are briefly introduced.

Prelude

Hydrodynamic stability concerns the stability and instability of motions of fluids.

The concept of stability of a state of a physical or mathematical system was understood in the eighteenth century, and Clerk Maxwell (see Campbell & Garnett, 1882, p. 440) expressed the qualitative concept clearly in the nineteenth:

So hydrodynamic stability is an important part of fluid mechanics, because an unstable flow is not observable, an unstable flow being in practice broken down rapidly by some ‘small variation’ or another. Also unstable flows often evolve into an important state of motion called turbulence, with a chaotic three-dimensional vorticity field with a broad spectrum of small temporal and spatial scales called turbulence.