1,461 research outputs found
Topological Segmentation of 2D Vector Fields
Vector field topology has a long tradition as a visualization tool. The separatrices segment the domain visually into
canonical regions in which all streamlines behave qualitatively
the same. But application scientists often need more than just a
nice image for their data analysis, and, to best of our knowledge,
so far no workflow has been proposed to extract the critical
points, the associated separatrices, and then provide the induced
segmentation on the data level.
We present a workflow that computes the segmentation of the
domain of a 2D vector field based on its separatrices. We show
how it can be used for the extraction of quantitative information
about each segment in two applications: groundwater flow and
heat exchange
Master of Science
thesisAnalysis and visualization of flow is an important part of many scientific endeavors. Computation of streamlines is fundamental to many of these analysis and visualization tasks. A streamline is the path a massless particle traces under the instantenous velocities of a given vector field. Flow data are often stored as a sampled vector field over a mesh. We propose a new representation of flow defined by such a vector field. Given a triangulation and a vector field defined over its vertices, we represent flow in the form of its transversal behavior over the edges of the triangulation. A streamline is represented as a set of discrete jumps over these edges. Any information about the actual path taken through the interior of the triangles is discarded. We eliminate the necessity to compute actual paths of streamlines through the interior of each triangle while maintaining the aggregate behavior of flow within each of them. We discretize each edge uniformly into a fixed number of bins and use this discretization to form a combinatorial representation of flow in the form of a directed graph whose nodes are the set of all bins and its edges represent the discrete jumps between these bins. This representation is a combinatorial structure that provides robustness and consistency in expressing flow features like the critical points, streamlines, separatrices and closed streamlines which are otherwise hard to compute consistently
Dynamic Topology in Spatiotemporal Chaos
By measuring the tracks of tracer particles in a quasi-two-dimensional spatiotemporally chaotic laboratory flow, we determine the instantaneous curvature along each trajectory and use it to construct the instantaneous curvature field. We show that this field can be used to extract the time-dependent hyperbolic and elliptic points of the flow. These important topological features are created and annihilated in pairs only above a critical Reynolds number that is largest for highly symmetric flows. We also study the statistics of curvature for different driving patterns and show that the curvature probability distribution is insensitive to the details of the flow
Objective Momentum Barriers in Wall Turbulence
We use the recent frame-indifferent theory of diffusive momentum transport to
identify internal barriers in wall-bounded turbulence. Formed by the invariant
manifolds of the Laplacian of the velocity field, the barriers block the
viscous part of the instantaneous momentum flux in the flow. We employ the
level sets of single-trajectory Lagrangian diagnostic tools, the trajectory
rotation average and trajectory stretching exponent, to approximate both
vortical and internal wall-parallel momentum transport barrier (MTB)
interfaces. These interfaces provide frame-indifferent alternatives to classic
velocity-gradient-based vortices and boundaries between uniform momentum zones
(UMZs). Indeed, we find that these elliptic manifold approximations and MTBs
also significantly outperform standard vortices and UMZ interfaces in blocking
diffusive momentum transport.Comment: 26 Pages, 14 Figur
Lagrangian analysis of fluid transport in empirical vortex ring flows
In this paper we apply dynamical systems analyses and computational tools to fluid transport in empirically measured vortex ring flows. Measurements of quasisteadily propagating vortex rings generated by a mechanical piston-cylinder apparatus reveal lobe dynamics during entrainment and detrainment that are consistent with previous theoretical and numerical studies. In addition, the vortex ring wake of a free-swimming Aurelia aurita jellyfish is measured and analyzed in the framework of dynamical systems to elucidate similar lobe dynamics in a naturally occurring biological flow. For the mechanically generated rings, a comparison of the net entrainment rate based on the present methods with a previous Eulerian analysis shows good correspondence. However, the current Lagrangian framework is more effective than previous analyses in capturing the transport geometry, especially when the flow becomes more unsteady, as in the case of the free-swimming jellyfish. Extensions of these results to more complex flow geometries is suggested
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