TABLE OF CONTENTS In Chapters 4 we have introduced the reader to the solution of incompressible flow problems and have illustrated these with many examples of Newtonian (Chapter 4) and non-Newtonian (Chapter 5) flows. In the present chapter, we shall address two separate topics of incompressible flow, which were not dealt with in the previous chapters. This chapter is thus divided into two parts. The common theme is that of the action of the body force due to gravity. We start with a section addressed to problems of free surfaces and continue with the second section, which deals with buoyancy effects caused by temperature differences in various parts of the domain.
The first part of this chapter, Sec. 6.2, will deal with problems in which a free surface of flow occurs when gravity forces are acting throughout the domain. Typical examples here would be for instance given by the disturbance of the free surface of water and the creation of waves by moving ships or submarines. Of course other problems of similar kinds arise in practice. Indeed in Chapter 10, where we deal with shallow water flows, a free surface is an essential condition but other assumptions and simplification have to be introduced. In the present chapter, we shall deal with the full incompressible flow equations without any further physical assumptions. There are other topics of free surfaces which occur in practice. One of these for instance is that of mould filling, which is frequently encountered in manufacturing where a particular...
