Boundary-Layer Separation in Unsteady Flow

Extension of the familiar concept of boundary-layer separation to flow along moving walls and unsteady flows is a subject that attracted some interest in the 1950's and has been investigated further in the past few years. The well-known criterion of vanishing wall-shear does not apply in such flows, and therefore the definition of the phenomenon becomes more difficult than in the simpler types of flow considered by Prandtl. The practical importance of extending the concept is discussed and arguments in favor of its definition in terms of Goldstein's singularity are reviewed. The model proposed by the present authors in 1971 is described, together with available numerical and experimental evidence that supports it. Numerical studies of steady and unsteady separating boundary-layer flows are reported, in which singularities of Goldstein's type are detected and comparisons can be made between the position-vs.-time curves of the singularity and of the point of vanishing wall-shear. One of these studies involves the classic case of the circular cylinder started impulsively, which was treated by Blasius and by Goldstein and Rosenhead and for which detailed numerical results are available. The distinction between vanishing wall-shear and separation is dramatic. This review closes with some remarks about the mathematical state of this subject.