ON THE NATURE OF SINGULARITIES INHERENT, UNDER A GIVEN ANALYTIC DISTRIBUTION OF THE EXTERNAL-PRESSURE, IN SOLUTIONS OF THE PRANDTL EQUATIONS NEAR THE POINT OF SEPARATION

A comprehensive analysis of a classical two-dimensional boundary layer is developed with the aim of revealing possible types of singularitie s related to separation. According to the basic assumption, the limit flow regime with a singular point of vanishing skin friction obeys an analytic solution where the frictional intensity approaches zero accor ding to quadratic law rather than varing linearly with distance. Small deviations from the limit regime are described in terms of eigenfunct ions, three of which involve singularities. The flow field for all sup ercritical regimes is continued into a small region centered about the singular characteristic springing from the point of vanishing skin fr iction in the undisturbed limit solution. The solvability condition fo r a key boundary-value problem posed in this region as a result of mat ching the global-scaled solution upstream gives three different types of singularities of the Prandtl equation. According to the weakest-typ e singularity the skin friction varies as the square root of the cube of the local distance. The next type includes a sudden change in the w all shear stress derivative with respect to the coordinate along the s olid surface, it was ruled out of the basic limit solution. Then the f amous Landau-Goldstein singularity with the skin friction being propor tional to the square root of the local distance evolves. A still more complicated flow pattern may be composed of the singularity with a sud den change in the wall shear stress derivative superseded by the Landa u-Goldstein singularity at some small distance downstream. A qualitati ve comparison between theoretical predictions and experimental data fo r a circular cylinder in an incompressible stream is made with the emp hasis on conceivable explanations for the nonmonotonic behavior of fri ctional intensities in the transitional range of Reynolds numbers.