A. Boundary-layer concept

In Section 15872 it was shown that in real fluid flows the Reynolds number Re is the most important parameter. It is the dimensionless group containing the viscosity.

In many practical flow situations the Reynolds number is rather high, that is, of the order of 1,000 and more. Therefore, it is appropriate to study the asymptotic behavior of the solutions of the flow equations for the limit Re → ∞.

In 1904 L. Prandtl developed the boundary-layer concept for flows past bodies at high Reynolds numbers. According to this concept, the entire flow field can be divided into two different regions. In the larger of these two regions, which is almost the entire flow field, the viscosity can be neglected. In other words, the flow is inviscid in this region. The second region is a very narrow layer close to the wall, the boundary layer, which can be laminar or turbulent. The thickness δ of the boundary layer is extremely small. The following estimates can be made:

\[\label{eq1} \begin{array}{c} \delta\sim \mbox{Re}^{-1/2}\; \mbox{(laminar)}\\ \\ \delta \sim (\ln \mbox{Re})^{-1}\;\mbox{(turbulent)} \end{array} \tag{1}\]