OVERVIEW

There is a class of flows wherein the curl of the vorticity or the vorticity itself virtually vanishes everywhere except within thin layers or columns of fluid that wrap around or trail behind solid boundaries, free surfaces, or fluid interfaces, or even within compact regions that either are attached to the boundaries or are located in the bulk of the fluid. The equation of motion shows that the viscous force exerted on a small fluid parcel is small outside these regions and may thus be neglected, but makes important contributions within these regions and should be retained.

An important consequence of dropping the viscous force in the Navier Stokes equation, obtaining Euler's equation, is that the order of the governing system of equations with respect to the spatial partial derivatives is reduced from two to one. This makes it impossible, in general, to satisfy three scalar boundary conditions over each boundary as required for viscous fluids. The presence of boundary layers within which the motion of the fluid is governed by a second-order partial differential equation is thus necessary for the uncompromised description of the flow. Conversely, viscous forces may not be generally neglected uniformly throughout a bounded domain of a flow.

One class of boundary layers occur in high-Reynolds-number flow past a streamlined body such as an airfoil, or flow past a body that does not have too much of a bluff shape such as a cylinder or a sphere. Prandtl (1904) argued that, at sufficiently high Reynolds numbers,...