Topological Methods in Data Analysis and Visualization VI, Springer, 2020, pp. 133-157
Abstract
Dynamical systems, such as the second-order ODEs that govern the motion of finite-sized objects in fluids, describe the evolution of a state by a trajectory living in a high-dimensional phase space. The high dimensionality leads to visualization challenges and, for the case of inertial particles, multiple models exist that pose different assumptions. In this paper, we thoroughly address the extraction of a specific feature, namely the vortex corelines of inertial particles. Based on a general template model that comprises two of the most commonly used inertial particle ODEs, we first transform their high-dimensional tangent vector field into a Galilean reference frame in which the observed inertial particle flow becomes as steady as possible. In the optimal frame, we derive first-order and second-order vortex coreline criteria, allowing us to extract straight and bent inertial vortex corelines using 3D and 6D parallel vectors operators, respectively. With this, we generalize existing work in multiple ways: not only do we handle two inertial particle models at once, we extend the concept of second-order vortex corelines to the inertial case and make them Galilean-invariant by deriving the criteria from a steady reference frame, rather than from a geometric characterization.
