Topological classification of flow separation on three-dimensional bodies

In the study of three-dimensional, separated flows, a topological approach to separation and a phenomenological approach have been considered. The topological approach is based on ideas of Poincare (1928), while the phenomenological approach distinguishes between 'open' and 'closed' separation as posed by Wang (1974). In the present paper, the topological description provided by Legendre (1956, 1965, 1982) is considered, taking into account its utilization by Tobak and Peake (1979, 1982). An attempt is made to provide a more complete framework for the description of separated as well as attached flows. Nomenclature is introduced to describe the topology of the skin-friction-line portraits on a three-dimensional body. The topological ideas are illustrated by the use of hypothetical oil-flow experiments supplemented with actual flow-visualization data when possible.