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
Ev. Bogdanovaryzhova et Os. Ryzhov, 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, Theoretical and computational fluid dynamics, 6(4), 1994, pp. 193-212
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den change in the wall shear stress derivative superseded by the Landa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.