Advected Tangent Curves: A General Scheme for Characteristic Curves of Flow Fields

We present the first general scheme to describe all four types of characteristic curves of flow fields – stream, path, streak, and time lines – as tangent curves of a derived vector field. Thus, all these lines can be obtained by a simple integration of an autonomous ODE system. Our approach draws on the principal ideas of the recently introduced tangent curve description of streak lines. We provide the first description of time lines as tangent curves of a derived vector field, which could previously only be constructed in a geometric manner. Furthermore, our scheme gives rise to new types of curves. In particular, we introduce advected stream lines as a parameter‐free variant of the time line metaphor. With our novel mathematical description of characteristic curves, a large number of feature extraction and analysis tools becomes available for all types of characteristic curves, which were previously only available for stream and path lines. We will highlight some of these possible applications including the computation of time line curvature fields and the extraction of cores of swirling advected stream lines.