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) 2 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 2

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 3

4. Vortex detection - more recent work Lagrangian type methods: –Non-local swirl [Cucitore 1999] –Objective criterion M z [Haller 2005] Better than 2 ? 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 4

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 5

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

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

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

9. Radii of vortex core lines Dagstuhl Seminar Scientific Visualization, July 15-20, 2007 9 Steady flowUnsteady flow Levy et al. Sujudi / Haimes Higher-order Correct adapted methods

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 10

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

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 12