Boundary Layers and Related Topics

Abstract

The reason for the occurrence of boundary layers and their role in high Reynolds number flows have been considered in Section 8.3. However, the fact that flow outside the boundary layers is irrotational (Section 10.3) provides another way of viewing the process of boundary layer formation. Fluid particles can acquire vorticity only by viscous diffusion (i.e. through the action of the term ν ∇ ² σ in equation (6.26)). The action of viscosity comes in at the boundary through the need to satisfy the no-slip condition. As a result vorticity is introduced into the flow at the boundary, and then diffuses away from it. The boundary layer can be defined as the region of appreciable vorticity. The boundary layer is long and thin (L ≤ δ) when the fluid travels a long distance downstream during the time that the vorticity diffuses only a small distance away from the boundary. This happens when the Reynolds number is large.