Toward a Lagrangian Vector Field Topology

In this paper we present an extended critical point concept which allows us to apply vector field topology in the case of unsteady flow. We propose a measure for unsteadiness which describes the rate of change of the velocities in a fluid element over time. This measure allows us to select particles for which topological properties remain intact inside a finite spatio-temporal neighborhood. One benefit of this approach is that the classification of critical points based on the eigenvalues of the Jacobian remains meaningful. In the steady case the proposed criterion reduces to the classical definition of critical points. As a first step we show that finding an optimal Galilean frame of reference can be obtained implicitly by analyzing the acceleration field. In a second step we show that this can be extended by switching to the Lagrangian frame of reference. This way the criterion can detect critical points moving along intricate trajectories. We analyze the behavior of the p...

• Type: Journal
• Year: 2010
• Where: CGF
• Authors: Raphael Fuchs, Jan Kemmler, Benjamin Schindler, Jürgen Waser, Filip Sadlo, Helwig Hauser, Ronald Peikert
• Keywords: CGF 2008, CGF 2010, Critical Points, Extended Critical Point, finite Spatio-temporal Neighborhood