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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 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) Batchelor (1950, 1952) Significant work in last decade Turbulent Relative Dispersion
Seed flow with tracer particles Locate tracers optically Multiple cameras 3D coordinates Follow tracers in time Lagrangian Particle Tracking Exp. Fluids40:301, 2006
Swirling flow between counter-rotating disks Baffled disks: inertial forcing Two 1 kW DC motors Temperature controlled Experimental Facility
Two forcing modes Pumping and Shearing Statistical stagnation point in center Anisotropic and inhomogeneous flow High Reynolds number: Large-scale flow R = 200 - 815
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
Inertial range scaling theory r(t) = separation between a pair of particles Pair Separation Rate
Results R = 815 Science311:835, 2006
Results R = 815 Science311:835, 2006
Batchelor’s Timescale Not a full collapse when scaled by Science311:835, 2006
Batchelor’s Timescale Collapse in space and time when scaled by t0 Not a full collapse when scaled by Science311:835, 2006
Deviation Time • t* = time until 5% deviation from Batchelor law • R = 200 815 • t* = 0.071 t0 New J. Phys.8:109, 2006
Higher-order corrections? Can this deviation be explained by adding a correction term?
Higher-order corrections? Can this deviation be explained by adding a correction term?
Velocity-Acceleration SF Should have Mann et al. 1999 Hill 2006
Velocity-Acceleration SF Should have
Components Longitudinal Transverse
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:
Raw Measurement New J. Phys.8:109, 2006
Subtraction of Initial Separation • Experimentally, we can consider , where to approximate dispersion from a point source
Subtracted Measurement New J. Phys.8:109, 2006
Subtracted Measurement New J. Phys.8:109, 2006
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:
Results New J. Phys.8:109, 2006 R = 815 = 1.05 Raw exit times
Results New J. Phys.8:109, 2006 Subtracted exit times Raw exit times
Richardson Constant? New J. Phys.8:109, 2006 Subtracted exit times Raw exit times
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?