Structural Stability in Evolving Flow Fields

Abstract

The changing topology of an evolving flow field can be studied by mapping it into velocity space and observing the singularities. In two dimensions the structurally stable singularities are folds, which are lines, and cusps, which are isolated points on the folds [2]. In three dimensions they are fold surfaces, which contain ribs, and the ribs themselves may contain isolated singular points. As the field changes with time these singularities interact to produce events. Between events the basic structure of the flow field remains the same. How many different kinds of event will occur generically depends on whether or not the flow field is constrained (for instance by being irrotational); the catalogue of events can be deduced from known results on stable mappings and from catastrophe theory. The paper is mainly a summary of previously published results [1,6].