TABLE OF CONTENTS In the preceding chapters we discussed a variety of analytical and numerical methods for computing the structure of steady and unsteady flows under a broad range of conditions, including flows at low Reynolds numbers, irrotational flows, and flows that are dominated by vortex motions. In this chapter we address the important question of whether these flows can be realized in practice.
In nature and technology, a flow is established necessarily through a transient process beginning from a certain initial condition, and subject to the imposed boundary conditions. The fact that the boundary conditions may be consistent with a particular steady or unsteady state that is describable in analytical or numerical form does not guarantee that that state will be established. For instance, imposing a constant pressure drop across the length of a circular tube does not guarantee the onset of unidirectional Poiseuille flow with a parabolic velocity profile discussed in Section 5.1. On the contrary, as early as 1883, Reynolds observed that, at sufficiently high Reynolds numbers, the flow develops wavy motions and becomes turbulent, and the assumption of steady unidirectional motion ceases to be valid.
Furthermore, flows in industrial, laboratory, or natural settings are subjected to small-amplitude disturbances due to a variety of reasons including equipment vibration and Brownian motion of microscopic suspended particles. In fact, in certain technological applications, perturbations are purposely introduced into the flow in order to initiate a desired type of action, such as to enhance fluid mixing or delay boundary-layer separation. It is...
