1. Experimental Studies of Turbulent Relative Dispersion N. T. Ouellette H. Xu M. Bourgoin E. Bodenschatz N. T. Ouellette H. Xu M. Bourgoin E. Bodenschatz

2. Turbulent Relative Dispersion Separation of fluid element pairs Closely related to turbulent mixing and transport Relevant to a wide range of applied problems Separation of fluid element pairs Closely related to turbulent mixing and transport Relevant to a wide range of applied problems Long history Richardson (1926) Batchelor (1950, 1952) Significant work in last decade Long history Richardson (1926) Batchelor (1950, 1952) Significant work in last decade

3. Lagrangian Particle Tracking Seed flow with tracer particles Locate tracers optically Multiple cameras  3D coordinates Follow tracers in time Seed flow with tracer particles Locate tracers optically Multiple cameras  3D coordinates Follow tracers in time Exp. Fluids 40:301, 2006

4. Experimental Facility Swirling flow between counter-rotating disks Baffled disks: inertial forcing Two 1 kW DC motors Temperature controlled Swirling flow between counter-rotating disks Baffled disks: inertial forcing Two 1 kW DC motors Temperature controlled

5. Large-scale flow Two forcing modes Pumping and Shearing Statistical stagnation point in center Anisotropic and inhomogeneous flow High Reynolds number: Two forcing modes Pumping and Shearing Statistical stagnation point in center Anisotropic and inhomogeneous flow High Reynolds number: R = 200 - 815

6. Experimental parameters 5 x 5 x 5 cm 3 measurement volume 25  m polystyrene microspheres High-speed CMOS cameras Phantom v7.1 27 kHz 256 x 256 pixels 5 x 5 x 5 cm 3 measurement volume 25  m polystyrene microspheres High-speed CMOS cameras Phantom v7.1 27 kHz 256 x 256 pixels Illumination 2 pulsed Nd:YAG lasers ~130 W laser light Illumination 2 pulsed Nd:YAG lasers ~130 W laser light

8. Pair Separation Rate Inertial range scaling theory r(t) = separation between a pair of particles Inertial range scaling theory r(t) = separation between a pair of particles

9. Results R = 815 Science 311:835, 2006

10. Results R = 815 Science 311:835, 2006

11. Batchelor’s Timescale Not a full collapse when scaled by   Science 311:835, 2006

12. Batchelor’s Timescale Not a full collapse when scaled by   Collapse in space and time when scaled by t 0 Science 311:835, 2006

13. Deviation Time t* = time until 5% deviation from Batchelor law R = 200  815 t* = 0.071 t 0 t* = time until 5% deviation from Batchelor law R = 200  815 t* = 0.071 t 0 New J. Phys. 8:109, 2006

14. Higher-order corrections? Can this deviation be explained by adding a correction term?

15. Higher-order corrections? Can this deviation be explained by adding a correction term?

16. Velocity-Acceleration SF Should have Mann et al. 1999 Hill 2006 Mann et al. 1999 Hill 2006

17. Velocity-Acceleration SF Should have

18. Components Longitudinal Transverse

19. Modified Batchelor law

20. Distance Neighbor Function Spherically-averaged PDF of the pair separations Introduced by Richardson (1926) Spherically-averaged PDF of the pair separations Introduced by Richardson (1926) Governed by a diffusion-like equation Solutions assume dispersion from a point source Governed by a diffusion-like equation Solutions assume dispersion from a point source Richardson: Batchelor: Implies t 3 law!

21. Raw Measurement New J. Phys. 8:109, 2006

22. Subtraction of Initial Separation Experimentally, we can consider, where to approximate dispersion from a point source Experimentally, we can consider, where to approximate dispersion from a point source

23. Subtracted Measurement New J. Phys. 8:109, 2006

24. Subtracted Measurement New J. Phys. 8:109, 2006

25. Fixed-Scale Statistics Consider time as a function of space Define thresholds r n =  n r 0 Compute time t  (r n ) for separation to grow from r n to r n+1 Prediction: Consider time as a function of space Define thresholds r n =  n r 0 Compute time t  (r n ) for separation to grow from r n to r n+1 Prediction:

26. Results Raw exit times R = 815  = 1.05 R = 815  = 1.05 New J. Phys. 8:109, 2006

27. Results Raw exit times Subtracted exit times New J. Phys. 8:109, 2006

28. Richardson Constant? Raw exit times Subtracted exit times New J. Phys. 8:109, 2006

29. Conclusions Observation of robust Batchelor regime t 0 is an important parameter Distance neighbor function shape depends strongly on scale Exit times are inconclusive for our data Higher Reynolds numbers? Observation of robust Batchelor regime t 0 is an important parameter Distance neighbor function shape depends strongly on scale Exit times are inconclusive for our data Higher Reynolds numbers?