This paper presents an approach to a time-dependent variant of the concept of vector field topology for 2D vector fields. Vector field topology is defined for steady vector fields and aims at discriminating the domain of a vector field into regions of qualitatively different behavior. The presented approach represents a generalization for saddletype critical points and their separatrices to unsteady vector fields based on generalized streak lines, with the classical vector field topology as its special case for steady vector fields. The concept is closely related to that of Lagrangian coherent structures obtained as ridges in the finite-time Lyapunov exponent field. The proposed approach is evaluated on both 2D time-dependent synthetic and vector fields from computational fluid dynamics.

LCS, FTLE, time dependent vector field topology, generalized streak lines, hyperbolic trajectories, space-time streak manifolds

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