20 Introduction

In this chapter we wish to consider the stability of steady two-dimensional or axisymmetric flows with parallel streamlines. Flows of this type were first studied experimentally by Reynolds (1883), who observed that instability could occur in quite different ways depending on the form of the basic velocity distribution. Thus, when the velocity profile is of the form shown in Fig. 4.1(a) he observed that eddies showed themselves reluctantly and irregularly whereas when the profile is as shown in Fig. 4.1(b) the eddies appeared in the middle regularly and readily . From these observations he was led to consider the role of viscosity in flows of this type. By comparing the flow of a viscous fluid with that of an inviscid fluid, both flows being assumed to have the same basic velocity distribution, he was led to formulate two fundamental hypotheses which can be stated as follows:

• First Hypothesis. The inviscid fluid may be unstable and the viscous fluid stable. The effect of viscosity is then purely stabilizing.

• Second Hypothesis. The inviscid fluid may be stable and the viscous fluid unstable. In this...