Objective Vortex Corelines of Finite-sized Objects in Fluid Flows

Vortices are one of the most-frequently studied phenomena in fluid flows. The center of the rotating motion is called the vortex coreline and its successful detection strongly depends on the choice of the reference frame. The optimal frame moves with the center of the vortex, which incidentally makes the observed fluid flow steady and thus standard vortex coreline extractors such as Sujudi-Haimes become applicable. Recently, an objective optimization framework was proposed that determines a near-steady reference frame for tracer particles. In this paper, we extend this technique to the detection of vortex corelines of inertial particles. An inertial particle is a finite-sized object that is carried by a fluid flow. In contrast to the usual tracer particles, they do not move tangentially with the flow, since they are subject to gravity and exhibit mass-dependent inertia. Their particle state is determined by their position and own velocity, which makes the search for the optimal frame a high-dimensional problem. We demonstrate in this paper that the objective detection of an inertial vortex coreline can be reduced in 2D to a critical point search in 2D. For 3D flows, however, the vortex coreline criterion remains a parallel vectors condition in 6D. To detect the vortex corelines we propose a recursive subdivision approach that is tailored to the underlying structure of the 6D vectors. The resulting algorithm is objective, and we demonstrate the vortex coreline extraction in a number of 2D and 3D vector fields.