Topology of surface shear-stress lines

The topography of surface shear-stress lines on a three-dimensional body topologically equivalent to a sphere has been studied on the basis of simple topological rules. The main points discussed and the concepts introduced are the topological similarity among different patterns and their standard representations on a plane, the structural stability as a discriminating principle of selection among different patterns and the gradual merging principle as an intuitive way of constructing sequences of patterns connected to the variation of external conditions. A brief discussion of some theoretical and experimental patterns deduced from the literature has been done in order to illustrate these points.