Finite-Time Transport Structures of Flow Fields

Modern experimental and computational fluid mechanics are increasingly concerned with the structure nature of fluid motion. Recent research has highlighted the analysis of one transport structure which is called Lagrangian coherent structure. However, the quantity nature of the flow transport is still unclear. In this paper, we focus on the transport characteristics of physical quantities and propose an approach to visualize the finite-time transport structure of quantity advection. This is similar to an integral convolution over a scalar field along path-lines of a flow field. Applied to a well-chosen set of physical quantity fields this yields structures giving insights into the dynamical processes of the underlying flow. We demonstrate our approach on a number of test data sets.

[1]  G. Haller.  Lagrangian coherent structures from approximate velocity data , 2002 .

[2]  Robert S. Laramee,et al.  The State of the Art in Flow Visualization: Dense and Texture‐Based Techniques , 2004, Comput. Graph. Forum.

[3]  A. Fuller,et al.  Stability of Motion , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Filip Sadlo,et al.  Visualizing Lagrangian Coherent Structures and Comparison to Vector Field Topology , 2009, Topology-Based Methods in Visualization II.

[5]  Filip Sadlo,et al.  Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction , 2007, IEEE Transactions on Visualization and Computer Graphics.

[6]  David L. Kao,et al.  UFLIC: a line integral convolution algorithm for visualizing unsteady flows , 1997 .

[7]  George Haller,et al.  Geometry of Cross-Stream Mixing in a Double-Gyre Ocean Model , 1999 .

[8]  V. S. Vaidhyanathan,et al.  Transport phenomena , 2005, Experientia.

[9]  Hans Hagen,et al.  Visualization of Coherent Structures in Transient 2D Flows , 2009, Topology-Based Methods in Visualization II.

[10]  Brian Cabral,et al.  Imaging vector fields using line integral convolution , 1993, SIGGRAPH.

[11]  Peter Hastreiter,et al.  Interactive exploration of volume line integral convolution based on 3D-texture mapping , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[12]  Kwan-Liu Ma,et al.  Visualizing vector fields using line integral convolution and dye advection , 1996, Proceedings of 1996 Symposium on Volume Visualization.

[13]  Gordon Erlebacher,et al.  Particle and texture based spatiotemporal visualization of time-dependent vector fields , 2005, VIS 05. IEEE Visualization, 2005..

[14]  Gerik Scheuermann,et al.  Eyelet particle tracing - steady visualization of unsteady flow , 2005, VIS 05. IEEE Visualization, 2005..

[15]  G. Haller.  An objective definition of a vortex , 2004, Journal of Fluid Mechanics.

[16]  Hans Hagen,et al.  Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications , 2007, IEEE Transactions on Visualization and Computer Graphics.

[17]  Hans-Peter Seidel,et al.  Extraction of parallel vector surfaces in 3D time-dependent fields and application to vortex core line tracking , 2005, VIS 05. IEEE Visualization, 2005..

[18]  David C. Banks,et al.  A Predictor-Corrector Technique for Visualizing Unsteady Flow , 1995, IEEE Trans. Vis. Comput. Graph..

[19]  Hans-Peter Seidel,et al.  Feature Flow Fields , 2003, VisSym.

[20]  Hans Hagen,et al.  Topology tracking for the visualization of time-dependent two-dimensional flows , 2002, Comput. Graph..

[21]  David C. Banks,et al.  Vortex tubes in turbulent flows: identification, representation, reconstruction , 1994, Proceedings Visualization '94.

[22]  Xavier Tricoche,et al.  Tracking of vector field singularities in unstructured 3D time-dependent datasets , 2004, IEEE Visualization 2004.

[23]  Ronald Peikert,et al.  Vortex Tracking in Scale-Space , 2002, VisSym.

[24]  Hans-Peter Seidel,et al.  Path Line Attributes - an Information Visualization Approach to Analyzing the Dynamic Behavior of 3D Time-Dependent Flow Fields , 2009, Topology-Based Methods in Visualization II.

[25]  G. Haller.  Distinguished material surfaces and coherent structures in three-dimensional fluid flows , 2001 .

[26]  J. Marsden,et al.  Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows , 2005 .

[27]  Kwan-Liu Ma,et al.  Visualizing time-varying volume data , 2003, Comput. Sci. Eng..

[28]  G. Haller,et al.  Lagrangian coherent structures and mixing in two-dimensional turbulence , 2000 .

[29]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[30]  G. Haller.  Finding finite-time invariant manifolds in two-dimensional velocity fields. , 2000, Chaos.

[31]  Hans-Peter Seidel,et al.  Topological methods for 2D time-dependent vector fields based on stream lines and path lines , 2005, IEEE Transactions on Visualization and Computer Graphics.

[32]  Hans-Peter Seidel,et al.  Eurographics/ Ieee-vgtc Symposium on Visualization (2006) Path Line Oriented Topology for Periodic 2d Time-dependent Vector Fields , 2022 .

[33]  Hans-Christian Hege,et al.  amira: A Highly Interactive System for Visual Data Analysis , 2005, The Visualization Handbook.

[34]  Gordon Erlebacher,et al.  A texture-based framework for spacetime-coherent visualization of time-dependent vector fields , 2003, IEEE Visualization, 2003. VIS 2003..

[35]  Kwan-Liu Ma,et al.  Time-varying, multivariate volume data reduction , 2005, SAC '05.

[36]  Hans-Christian Hege,et al.  Fast and resolution independent line integral convolution , 1995, SIGGRAPH.