On the Extraction of Long-living Features in Unsteady Fluid Flows

This paper proposes aGalilean invariant generalization of critical points ofvector field topology for 2D time-dependent flows. The approach is based upon a Lagrangian consideration of fluid particle motion. It extracts long-living features, likesaddles and centers, and filters out short-living local structures. This is well suited for analysis ofturbulent flow, where standard snapshot topology yields an unmanageable large number of topological structures that are barely related to the few main long-living features employed in conceptual fluid mechanics models. Results are shown for periodic and chaoticvortex motion.

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

[2]  David J. Peake,et al.  Topology of Three-Dimensional Separated Flows , 1982 .

[3]  Lambertus Hesselink,et al.  Visualizing vector field topology in fluid flows , 1991, IEEE Computer Graphics and Applications.

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

[5]  Gilead Tadmor,et al.  Optimal mixing in recirculation zones , 2004 .

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

[7]  Robert S. Laramee,et al.  The State of the Art , 2015 .

[8]  S. Wiggins,et al.  An analytical study of transport, mixing and chaos in an unsteady vortical flow , 1990, Journal of Fluid Mechanics.

[9]  Hans-Peter Seidel,et al.  Finite-Time Transport Structures of Flow Fields , 2008, 2008 IEEE Pacific Visualization Symposium.

[10]  Jinhee Jeong,et al.  On the identification of a vortex , 1995, Journal of Fluid Mechanics.

[11]  HesselinkLambertus,et al.  Representation and Display of Vector Field Topology in Fluid Flow Data Sets , 1989 .

[12]  Gerik Scheuermann,et al.  Topology-based Methods in Visualization , 2007, Topology-based Methods in Visualization.

[13]  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.

[14]  Bilal Alsallakh,et al.  Delocalized Unsteady Vortex Region Detectors , 2008, VMV.

[15]  Frits H. Post,et al.  Detection, quantification, and tracking of vortices using streamline geometry , 2000, Comput. Graph..

[16]  Lambertus Hesselink,et al.  Representation and display of vector field topology in fluid flow data sets , 1989, Computer.

[17]  J. Hunt.  Vorticity and vortex dynamics in complex turbulent flows , 1987 .

[18]  Ronald Peikert,et al.  The "Parallel Vectors" operator-a vector field visualization primitive , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

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

[20]  Pierre Soille,et al.  Morphological Image Analysis , 1999 .

[21]  Hans-Christian Hege,et al.  Cores of Swirling Particle Motion in Unsteady Flows , 2007, IEEE Transactions on Visualization and Computer Graphics.

[22]  George Haller,et al.  Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence , 2001 .