Events in evolving three-dimensional vector fields

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Abstract
For a static three-dimensional vector field u=u(x) the set of singular points of the vector function forms a smooth two-dimensional surface embedded in the three-dimensional space of x. When this surface is mapped into the three-dimensional space a u there results a surface which typically contains sharp creases, and the shape of this surface characterises the structure of the vector field. As the field evolves with time this singular surface will change, and special points in space-time can be identified where the surface changes its shape in a fundamental way. These changes are called events. The possible events are identified and shown pictorially for general vector fields and for the special case of irrotational fields. The pattern of events gives a morphological way of comparing, say, an observed field with a computed field. If the two fields have the same pattern of events their structures are similar and they are evolving in similar ways.

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