  Vortex is a central concept in the understanding of turbulent dynamics.
Objective algorithms for the detection and extraction of vortex structures can
facilitate the physical understanding of turbulence regeneration dynamics by
enabling automated and quantitative analyses of these structures. Despite the
wide availability of vortex identification criteria, they only label spatial
regions belonging to vortices, without any information on the identity,
topology and shape of individual vortices. This latter information is stored in
the axis lines lining the contours of vortex tubes. In this study, a new
tracking algorithm is proposed which propagates along the vortex axis lines and
iteratively searches for new directions for growth. The method is validated in
flow fields from transient simulations where vortices of different shapes are
controllably generated. It is then applied to statistical turbulence for the
analysis of vortex configurations and distributions. It is shown to reliably
extract axis lines for complex three-dimensional vortices generated from the
walls. A new procedure is also proposed that classifies vortices into commonly
observed shapes, including quasi-streamwise vortices, hairpins, hooks and
branches, based on their axis-line topology. Clustering analysis is performed
on the extracted axis lines to reveal vortex organization patterns and their
potential connection to large-scale motions in turbulence.
