ABSTRACT
Boundary layers are flows formed in the close vicinity of solid boundaries. Their properties significantly differ from the properties of the flows further away from the boundaries; see figure 5.1. Boundary layers are most clearly defined for laminar flows with high Reynolds numbers, because in this case this will be the only part of the flow where viscosity is important, whereas the flow in the exterior is nearly ideal. One could roughly think that such an ideal flow is slowly varying (often irrotational) and satisfying the free-slip boundary conditions on the solid surface. In the other words, when finding the exterior flow, presence of the boundary layer can be ignored because it is much thinner than the typical length scale L in the exterior flow, δ L; see figure 5.1. On the other hand, the value of the velocity slip serves as a boundary condition at the top side of the thin boundary layer. The role of the viscosity here is to eliminate the free slip by slowing the velocity down to zero rapidly within a thin layer so that the no-slip boundary condition could be satisfied at the bottom side of the boundary layer. Since the viscosity coefficient is small, the velocity gradient in the boundary layer must be large so that the viscosity term would become sufficient to balance the other terms in the Navier-Stokes equation. For this reason the boundary layer is thinthinner than the curvature radius of the solid surface-and it can be locally thought as a plane-parallel shear flow. These ideas were originally presented in Prandtl’s 1905 paper [20] and they remain a conceptual basis for the modern boundary layer theory in laminar flows. Very good detailed presentation of the laminar boundary layer theory can be found in the Acheson’s book Elementary Fluid Dynamics [1] as well as in Essentials of Fluid Dynamics by L. Prandtl [21].
