Fundamentals of Boundary-Layer Theory

Abstract

Flows of fluids with low viscosity values and thus very high Reynolds numbers occur in many technical applications. As was shown in the examples from the last chapter, the limiting solution Re = ∞ is often a good approximation. A notable shortcoming of this limiting solution is that the no-slip condition is not satisfied, i.e. the velocities at the wall are not zero but are finite. The viscosity must be taken into account in order to satisfy the no-slip condition. This takes care of the velocity transition from the limiting solution’s finite value close to the wall to the value of zero directly at the wall. At large Reynolds numbers this transition takes place in a thin layer close to the wall, called by L. Prandtl (1904) the boundary layer or frictional layer. As will be shown, the boundary layer is thinner the higher the Reynolds number, i.e. the smaller the viscosity.