14 Introduction

Instability also occurs in a homogeneous fluid owing to the dynamical effects of rotation or of streamline curvature. Three important examples of flows which exhibit this type of centrifugal instability are shown in Fig. 3.1. They are Couette flow, in which the fluid is contained between two rotating coaxial cylinders; flow in a curved channel due to a pressure gradient acting around the channel; and the flow in a boundary layer on a concave wall. In the absence of curvature, the last two of these examples may exhibit the type of instability associated with parallel shear flows, which will be discussed in Chapter 4.

Fig. 3.1: (a) Couette flow. (b) Flow in a curved channel. (c) Flow in a boundary layer on a concave wall.

The instability of rotating flows was first considered by Rayleigh (1880, 1916b). He considered a basic swirling flow of an inviscid fluid which moves with angular velocity ?(r), an arbitrary function of the distance r from the axis of rotation. By a simple physical argument Rayleigh then derived his celebrated criterion for stability. Rayleigh s circulation criterion states that a necessary and sufficient condition...