The dilemma of defining a vortex

The problem of defining a vortex in a real fluid is discussed. The definition and identification of a vortex in unsteady motions is difficult since streamlines and pathlines are not invariant with respect to Galilean and rotational transformations. Recirculatory streamline patterns at a certain instant in time do not necessarily represent vortex motions in which fluid particles are moving around a common axis. Thus, instantaneous streamline patterns do not provide enough information to be used for the definition of a vortex. Extremal properties of the vorticity field are not helpful either, since a local extremum in the vorticity is not necessary for the existence of a vortex. A proposal for a definition based on pathlines is presented.