Singularities in unsteady boundary layers
Abstract
Singularities encountered in solutions of the thinshearlayer (boundarylayer) equations are examined. The point of zero surface shear stress is distinguished from points at which the rate of growth of shear layer thickness becomes large, which may be termed points of separation, but which do not represent mathematical singularities if the rate of growth is not infinite. A singularity has also been observed to occur above a point on the axis of the flow over a rotating disk in a counterrotating fluid. The Goldstein (1948) square root singularity, in which surface shear stress approaches zero, is shown to occur only in steady or quasisteady flows. All singularities discovered thus far can be attributed to the failure of the shear layer calculations to conserve Vcomponent momentum.
 Publication:

AIAA Journal
 Pub Date:
 July 1979
 DOI:
 10.2514/3.61225
 Bibcode:
 1979AIAAJ..17..790B
 Keywords:

 Boundary Layer Equations;
 Shear Layers;
 Singularity (Mathematics);
 Unsteady Flow;
 Momentum Theory;
 Roots Of Equations;
 Wall Flow;
 Fluid Mechanics and Heat Transfer