Subscribe
Issue No.04 - April (2011 vol.17)
pp: 412-425
Tobias Schafhitzel , Universität Stuttgart, Stuttgart
Kudret Baysal , Universität Stuttgart, Stuttgart
Mikael Vaaraniemi , Universität Stuttgart, Stuttgart
Ulrich Rist , Universität Stuttgart, Stuttgart
Daniel Weiskopf , Universität Stuttgart, Stuttgart
ABSTRACT
In this paper, we present a visualization and tracking system for coherent structures. For this purpose, we propose to consider shear stress—the stretching and shear of particles inside a flow—in vortex dynamics. Based on a discussion and comparison of recent methods for computing shear stress, we introduce visualization techniques in order to provide a representation of shear layers according to their physical interpretation. This paper contributes a combination of theory in fluid mechanics and the corresponding visualization: 1) shear layer criteria are assessed according to how well they can be combined with common vortex identification criteria; 2) sheets of maximal shear are introduced as an appropriate visual representation of shear layers; 3) a visualization method is described for simultaneous tracking of vortices and shear layers as well as their interaction; and 4) the relevance of shear layers in vortex dynamics is demonstrated by means of several examples. We have implemented these new techniques in an interactive visualization system for time-dependent 3D flow. The system is used by fluid mechanics experts in their research of shear-vortex interaction.
INDEX TERMS
Flow visualization, tracking, coherent structures, vortex dynamics, shear layers.
CITATION
Tobias Schafhitzel, Kudret Baysal, Mikael Vaaraniemi, Ulrich Rist, Daniel Weiskopf, "Visualizing the Evolution and Interaction of Vortices and Shear Layers in Time-Dependent 3D Flow", IEEE Transactions on Visualization & Computer Graphics, vol.17, no. 4, pp. 412-425, April 2011, doi:10.1109/TVCG.2010.65
REFERENCES
 [1] A. Babucke, M. Kloker, and U. Rist, "Numerical Investigation of Flow-Induced Noise Generation at the Nozzle End of Jet Engines," New Results in Numerical and Experimental Fluid Mechanics VI, C. Tropea, S. Jakirlic, H.-J. Heinemann, R. Henke, and H. Hönlinger, eds., vol. 96, pp. 413-420, Springer, 2007. [2] S. Bake, D. Meyer, and U. Rist, "Turbulence Mechanism in Klebanoff-Transition. A Quantitative Comparison of Experiment and Direct Numerical Simulation," J. Fluid Mechanics, vol. 459, pp. 217-243, 2002. [3] G. Baker and L. Pham, "A Comparison of Blob Methods for Vortex Sheet Roll-Up," J. Fluid Mechanics, vol. 547, pp. 297-316, 2006. [4] D.C. Banks and B.A. Singer, "A Predictor-Corrector Technique for Visualizing Unsteady Flow," IEEE Trans. Visualization and Computer Graphics, vol. 1, no. 2, pp. 151-163, July 1995. [5] K. Baysal and U. Rist, "Identification and Quantification of Shear Layer Influences on the Generation of Vortex Structures," New Results in Numerical and Experimental Fluid Mechanics VII, A. Dillmann, G. Heller, M. Klaas, H.-P. Kreplin, W. Nitsche, and W. Schröder, eds., Springer, 2010. [6] P. Chakraborty, S. Balachandar, and R. Adrian, "On the Relationships between Local Vortex Identification Schemes," J. Fluid Mechanics, vol. 535, pp. 189-214, 2005. [7] M. Chong, A. Perry, and B. Cantwell, "A General Classification of Three-Dimensional Flow Field," Physics of Fluids, vol. 2, pp. 765-777, 1990. [8] D. Eberly, Ridges in Image and Data Analysis. Computational Imaging and Vision. Kluwer Academic Publishers, 1996. [9] R. Griffiths and E. Hopfinger, "Coalescing of Geostrophic Vortices," J. Fluid Mechanics, vol. 178, pp. 73-97, 1987. [10] R.B. Haber and D.A. McNabb, "Visualization Idioms: A Conceptual Model for Visualization Systems," Visualization in Scientific Computing, G.M. Nielson, B.D. Shriver, and L.J. Rosenblum, eds., pp. 74-93, IEEE CS Press, 1990. [11] R. Haimes and D. Kenwright, "On the Velocity Gradient Tensor and Fluid Feature Extraction," Proc. AIAA 14th Computational Fluid Dynamics Conf., pp. 3288-3297, 1999. [12] G. Haller, "An Objective Definition of a Vortex," J. Fluid Mechanics, vol. 525, pp. 1-26, 2005. [13] R.M. Haralick, "Ridges and Valleys on Digital Images," Computer Vision, Graphics, and Image Processing, vol. 22, no. 1, pp. 28-38, 1983. [14] C.-M. Ho and P. Huerre, "Perturbed Free Shear Layers," Ann. Rev. of Fluid Mechanics, vol. 16, pp. 365-424, 1984. [15] J.C.R. Hunt, A.A. Wray, and P. Moin, "Eddies, Stream, and Convergence Zones in Turbulent Flows," Technical Report CTR-S88, Center for Turbulence Research, 1988. [16] J. Jeong and F. Hussain, "On the Identification of a Vortex," J. Fluid Mechanics, vol. 285, pp. 69-94, 1995. [17] M. Jiang, R. Machiraju, and D. Thompson, "Detection and Visualization of Vortices," The Visualization Handbook, C.D. Hansen and C.R. Johnson, eds., pp. 295-309, Elsevier, 2005. [18] V. Kolar, "Vortex Identification: New Requirements and Limitations," Int'l J. Heat and Fluid Flow, vol. 28, pp. 638-652, 2007. [19] A. Leonard, "Computing Three-Dimensional Incompressible Flows with Vortex Elements," Ann. Rev. of of Fluid Mechanics, vol. 17, pp. 523-559, 1985. [20] C. Lepage, T. Leweke, and A. Verga, "Spiral Shear Layers: Roll-Up and Incipient Instability," Physics of Fluids, vol. 17, no. 3, pp. 031705-1-031705-4, 2005. [21] H. Lugt, Vortex Flows in Nature and Technology. John Wiley & Sons, Inc., 1983. [22] I. Marusic, "Untravelling Turbulence Near Walls," J. Fluid Mechanics, vol. 630, pp. 1-4, 2009. [23] D. Meyer, "Direkte numerische Simulation nichtlinearer Transitionsmechanismen in der Strömungsgrenzschicht einer ebenen Platte," PhD thesis, Univ. Stuttgart, 2003. [24] H. Moffatt and A. Tsinober, "Topological Fluid Mechanics," Proc. IUTAM Symp., 1989. [25] R. Peikert and M. Roth, "The 'Parallel Vectors' Operator—A Vector Field Visualization Primitive," Proc. IEEE Conf. Visualization '99, pp. 263-270, 1999. [26] H. Pfister, M. Zwicker, J. van Baar, and M. Gross, "Surfels: Surface Elements as Rendering Primitives," Proc. ACM SIGGRAPH '00, pp. 335-342, 2000. [27] F. Ponta, "Effect of Shear-Layer Thickness on the Strouhal-Reynolds Number Relationship for Bluff-Body Wakes," J. Fluids and Structures, vol. 22, pp. 1133-1138, 2006. [28] H. Post, B. Vrolijk, R. Hauser, H. Laramee, and H. Doleisch, "The State of the Art in Flow Visualization: Feature Extraction and Tracking," Computer Graphics Forum, vol. 22, no. 4, pp. 775-792, 2003. [29] A. Provenzale, "Transport by Coherent Barotropic Vortices," Ann. Rev. of Fluid Mechanics, vol. 31, pp. 55-93, 1999. [30] P. Saffman, Vortex Dynamics. Cambridge Univ. Press, 1992. [31] J. Sahner, T. Weinkauf, N. Teuber, and H.-C. Hege, "Vortex and Strain Skeletons in Eulerian and Lagrangian Frames," IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 5, pp. 980-990, Sept./Oct. 2007. [32] T. Schafhitzel, K. Baysal, U. Rist, D. Weiskopf, and T. Ertl, "Particle-Based Vortex Core Line Tracking Taking into Account Vortex Dynamics," Proc. Int'l Symp. Flow Visualization '08, 2008. [33] T. Schafhitzel, J. Vollrath, J. Gois, D. Weiskopf, A. Castelo, and T. Ertl, "Topology-Preserving $\lambda_2$ -Based Vortex Core Line Detection for Flow Visualization," Computer Graphics Forum, vol. 27, no. 3, pp. 1023-1030, 2008. [34] D. Silver and X. Wang, "Tracking and Visualizing Turbulent 3D Features," IEEE Trans. Visualization and Computer Graphics, vol. 3, no. 2, pp. 129-141, June 1997. [35] S. Stegmaier, U. Rist, and T. Ertl, "Opening the Can of Worms: An Exploration Tool for Vortical Flows," Proc. IEEE Conf. Visualization '05, pp. 463-470, 2005. [36] H. Theisel, J. Sahner, T. Weinkauf, H.-C. Hege, and H.-P. Seidel, "Extraction of Parallel Vector Surfaces in 3D Time-Dependent Fields and Application to Vortex Core Line Tracking," Proc. IEEE Conf. Visualization '05, pp. 631-638, 2005. [37] H. Theisel and H.-P. Seidel, "Feature Flow Fields," Proc. EG/IEEE TCVG Symp. Visualization '03, pp. 141-148, 2003. [38] T. Weinkauf, J. Sahner, H. Theisel, and H.-C. Hege, "Cores of Swirling Particle Motion in Unsteady Flows," IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 6, pp. 1759-1766, Nov./Dec. 2007. [39] C. Williamson, "Vortex Dynamics in the Cylinder Wake," Ann. Rev. of of Fluid Mechanics, vol. 28, pp. 477-539, 1996. [40] J.-Z. Wu, A.-K. Xiong, and Y.-T. Yang, "Axial Stretching and Vortex Definition," Physics of Fluids, vol. 17, no. 3, pp. 038108-1-038108-4, 2005. [41] E. Zhang, H. Yeh, Z. Lin, and R.S. Laramee, "Asymmetric Tensor Analysis for Flow Visualization," IEEE Trans. Visualization and Computer Graphics, vol. 15, no. 1, pp. 106-122, Jan./Feb. 2009.