Folding points, flow instabilities and onset of vortex formation*

A Lagrangian finite-time diagnostic to identify distinct points of fluid material folding is introduced and applied in the analysis of several shear flows. By considering the deformation of lines of fluid particles over a finite integration time interval, their curvature change is used to quantify the strength of the fluid folding and central locations of the wrinkling at the onset of vortex formation. Because the curvature-based analysis combines the stretching and rotation of the fluid elements, distinct and subtle structures in the flow field can be highlighted after shorter integration intervals compared to classic strain-based Lagrangian visualization techniques, such as the finite-time Lyapunov exponent.

The approach is tested to capture the vortex formation in a temporally developing jet flow, an unstable separated shear flow over a cambered airfoil, and in the onset of a wake instability behind a circular cylinder. The kinematic finite-time approach has practical benefits for experiments that have only limited data available, and could potentially be applied to snapshots of streak lines that are recorded over a convenient time window.