Local behavior of streamlines in turbulent flows

Although streamlines have often been used mainly to visualize flow fields, they have been studied in recent years to some extent in the search for a better, more intuitive description and decomposition of the flow field. Streamlines seem a good candidate, as they are tangential to the velocity field and thus are prescribed by its structure. Similarly to the $Q$-$R$-classification of flow topologies, it is possible to classify the behavior of streamlines in an absolute sense by the unit vector gradient tensor and its first and second invariant $H$ and $K$. The invariants are found to have a physical interpretation, inasmuch as they are a measure for the local net convergence or divergence of the streamlines and its rate of change, respectively. The joint pdf of $H$ and $K$ is evaluated for different Reynolds-numbers from 119 to 330. It is found that streamlines expand rapidly while shrinking gently. As the local flow behavior is determined by the invariants, several quantities are conditioned on $H$ and $K$ in order to relate them to the structure of the flow.