If a solid-body contour (Figure 2.1) has a sharp corner forming a convex angle γ < π, then an incompressible fluid flow around it cannot be unseparated. It is well known that for unseparated flow over a convex corner an unrealistic situation arises, when the speed of fluid elements increases without limit as the corner is approached. According to potential-flow theory, the speed is proportional to r−α, where α = (π − γ)/(2π − γ), and r is the distance to the corner O. The pressure decreases as the point O is approached and, according to Bernoulli's law, must become negative in some vicinity of the point.
The physical reason for flow separation from a corner is the viscosity of the medium. If the flow around the corner remained unseparated, then the fluid acceleration ahead of the point O would be accompanied by a deceleration downstream of that point. The boundary layer next to the wall immediately behind the corner would then be subjected to an infinitely large adverse pressure gradient, which would lead to flow separation. There can be an exception in the case of slight surface bending, when the adverse pressure gradient proves to be insufficient for boundary-layer separation. This case will be considered in Section 3, devoted to determining the conditions for the onset of separation. As will be shown, the unseparated state of the flow near the corner is maintained up to angles π − γ = O(Re−1/4). A further increase of the surface bending angle π − γ leads to boundary-layer separation.