Some Solutions of the Viscous Flow Equations

Abstract

An obvious aim, once the equations of motion have been set up (in either the full form of Chapter 5 or in an approximate form such as those in Chapter 8) is to find solutions of them. Fluid dynamics thus constitutes an important branch of applied mathematics, although there are severe limitations to what can be learned by theory alone because of mathematical complexity, non-uniqueness, and instability. In this book, the mathematical aspects are somewhat underplayed to leave room for a full development of the experimental aspects. In this chapter we do look briefly at a few solutions of the Navier — Stokes equation and of the equation of creeping motion, both to illustrate the mathematical aspects of the subject and to provide information required elsewhere. For more systematic mathematical treatment see Refs. [12,13,14,15].