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Vortex detection in time-dependent flow

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Vortex detection in time-dependent flow. Ronny Peikert ETH Zurich. Vortex detection - early work. Derived from physical properties: vortex regions: Pressure Laplacian Q criterion (Okubo-Weiss, Hunt 1991) l 2 criterion (Jeong and Hussain, 1995) vortex axes (vortex core lines):

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  1. Vortex detection in time-dependent flow Ronny Peikert ETH Zurich

  2. Vortex detection - early work • Derived from physical properties: • vortex regions: • Pressure Laplacian • Q criterion (Okubo-Weiss, Hunt 1991) • l2 criterion (Jeong and Hussain, 1995) • vortex axes (vortex core lines): • Pressure&vorticity based (Banks and Singer, 1994) • Pressure valley line (Kida and Miura, 1997) These are valid for steady and unsteady flow! Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

  3. Vortex detection - early work (2) • Derived from geometric/topological properties: • vortex axes: • critical point analysis, separatrices (Helman and Hesselink 1991, Globus et al. 1991) • helicity-based, Levy et al. (1990) • streamline-based, Sujudi and Haimes (1995) • higher-order, Roth and Peikert (1998) These are just formulated for steady flow! But vortex axes are useful, complementary to vortex regions! Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

  4. Vortex detection - more recent work • Lagrangian type methods: • Non-local swirl [Cucitore 1999] • Objective criterion Mz [Haller 2005] Better than l2 ? • Time-dependent vortex axes methods: • Swirling particle motion [Weinkauf et al. 2007] • Work in progress [Bürger et al.] Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

  5. Adaptations of Sujudi-Haimes criterion • Sujudi-Haimes criterion (in parallel vectors formulation) AND filter criteria • Equivalent and more efficiently computable: AND filter criteria • Time-dependent version: AND filter criteria • Weinkauf et al. (2007) (equivalent formulation): AND filter criteria Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

  6. Tilting vortex example Sujudi-Haimes axis streamlines at t=0.3 pathlinesseeded at t=0.3 Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

  7. Vortex rope example Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

  8. Synthetic vortex rope streamlines pathlines Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

  9. Radii of vortex core lines adapted methods Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

  10. Comparisons Comparison of and : • Both reduce to Sujudi-Haimes criterion if flow is steady. • Criterion is Galilean invariant. • Consequently, it produces Sujudi-Haimes vortex core lines also in linearly moving frame of reference. • Visually indistinguishable in synthetic vortex rope and CFD vortex rope examples. • Criterion is possibly better in other CFD dataset examples. Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

  11. Comparisons (2) • Comparison (Tufo et al. '99) • mean velocity • rms velocity • pressure • spanwise vorticity • l2 • Vortex core line methods have problems with mixinglayer vortices • How about Mz ? Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

  12. Conclusion • Existing methods need further comparison • What degree of invariance is needed? Galilean? Objective? • We need a topology of time-dependent vector fields Dagstuhl Seminar Scientific Visualization, July 15-20, 2007