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Experimental Studies of Turbulent Relative Dispersion

Experimental Studies of Turbulent Relative Dispersion. N. T. Ouellette H. Xu M. Bourgoin E. Bodenschatz. Separation of fluid element pairs Closely related to turbulent mixing and transport Relevant to a wide range of applied problems. Long history Richardson (1926)

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Experimental Studies of Turbulent Relative Dispersion

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

  2. 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 Turbulent Relative Dispersion

  3. Seed flow with tracer particles Locate tracers optically Multiple cameras  3D coordinates Follow tracers in time Lagrangian Particle Tracking Exp. Fluids40:301, 2006

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

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

  6. 5 x 5 x 5 cm3 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 Experimental parameters

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

  8. Results R = 815 Science311:835, 2006

  9. Results R = 815 Science311:835, 2006

  10. Batchelor’s Timescale Not a full collapse when scaled by  Science311:835, 2006

  11. Batchelor’s Timescale Collapse in space and time when scaled by t0 Not a full collapse when scaled by  Science311:835, 2006

  12. Deviation Time • t* = time until 5% deviation from Batchelor law • R = 200  815 • t* = 0.071 t0 New J. Phys.8:109, 2006

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

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

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

  16. Velocity-Acceleration SF Should have

  17. Components Longitudinal Transverse

  18. Modified Batchelor law

  19. Spherically-averaged PDF of the pair separations Introduced by Richardson (1926) Governed by a diffusion-like equation Solutions assume dispersion from a point source Distance Neighbor Function Implies t3 law! Richardson: Batchelor:

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

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

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

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

  24. Fixed-Scale Statistics • Consider time as a function of space • Define thresholds rn = nr0 • Compute time t(rn) for separation to grow from rn to rn+1 • Prediction:

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

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

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

  28. Conclusions • Observation of robust Batchelor regime • t0 is an important parameter • Distance neighbor function shape depends strongly on scale • Exit times are inconclusive for our data • Higher Reynolds numbers?

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