Introduction

Previously, in Sections 4.5, 5.8 and 7.9, we saw that a uniformly flowing incompressible fluid that is modeled as being completely inviscid is incapable of exerting a drag force on a rigid stationary obstacle placed in its path. This result--which is known as d'Alembert's paradox--is surprising because, in practice, a stationary obstacle experiences a significant drag when situated in such a fluid, even in the limit that the Reynolds number tends to infinity (which corresponds to the inviscid limit). In this chapter, we shall attempt to reconcile these two results by introducing the concept of a boundary layer. This is a comparatively thin layer that covers the surface of an obstacle placed in a high Reynolds number incompressible fluid. Viscosity is assumed to have a significant effect on the flow inside the layer, but a negligible effect on the flow outside. For the sake of simplicity, we shall restrict our discussion to the two-dimensional boundary layers that form when a high Reynolds number fluid flows transversely around a stationary obstacle of infinite length and uniform cross-section. More information on such boundary layers can be found in Batchelor 2000 and Schlichting 1987.