Experimental Studies of Turbulent Relative Dispersion N. T. Ouellette H. Xu M. Bourgoin E. Bodenschatz
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Experimental Studies of Turbulent Relative
Dispersion
Experimental Studies of Turbulent Relative
Dispersion
N. T. OuelletteH. Xu
M. BourgoinE. Bodenschatz
N. T. OuelletteH. Xu
M. BourgoinE. Bodenschatz
Turbulent Relative DispersionTurbulent 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
Lagrangian Particle TrackingLagrangian 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, 2006Exp. Fluids 40:301, 2006
Experimental FacilityExperimental 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
Large-scale flowLarge-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 - 815R = 200 - 815
Experimental parametersExperimental parameters
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
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
Illumination 2 pulsed Nd:YAG
lasers ~130 W laser light
Pair Separation RatePair 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
ResultsResults
R = 815R = 815
Science 311:835, 2006Science 311:835, 2006
ResultsResults
R = 815R = 815
Science 311:835, 2006Science 311:835, 2006
Batchelor’s TimescaleBatchelor’s Timescale
Not a full collapse when scaled by
Not a full collapse when scaled by
Science 311:835, 2006Science 311:835, 2006
Batchelor’s TimescaleBatchelor’s Timescale
Not a full collapse when scaled by
Not a full collapse when scaled by
Collapse in space and time when
scaled by t0
Collapse in space and time when
scaled by t0
Science 311:835, 2006Science 311:835, 2006
Deviation TimeDeviation Time
t* = time until 5% deviation from Batchelor law
R = 200 815
t* = 0.071 t0
t* = time until 5% deviation from Batchelor law
R = 200 815
t* = 0.071 t0
New J. Phys. 8:109, 2006New J. Phys. 8:109, 2006
Higher-order corrections?Higher-order corrections?
Can this deviation be explained by adding a correction term?
Can this deviation be explained by adding a correction term?
Higher-order corrections?Higher-order corrections?
Can this deviation be explained by adding a correction term?
Can this deviation be explained by adding a correction term?
Velocity-Acceleration SFVelocity-Acceleration SF
Should have Should have
Mann et al. 1999Hill 2006Mann et al. 1999Hill 2006
Velocity-Acceleration SFVelocity-Acceleration SF
Should have Should have
ComponentsComponents
LongitudinalLongitudinalTransverseTransverse
Modified Batchelor lawModified Batchelor law
Distance Neighbor FunctionDistance 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:Richardson:
Batchelor:Batchelor:
Implies t3 law!Implies t3 law!
Raw MeasurementRaw Measurement New J. Phys. 8:109, 2006New J. Phys. 8:109, 2006
Subtraction of Initial SeparationSubtraction 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
Subtracted MeasurementSubtracted MeasurementNew J. Phys. 8:109, 2006New J. Phys. 8:109, 2006
Subtracted MeasurementSubtracted MeasurementNew J. Phys. 8:109, 2006New J. Phys. 8:109, 2006
Fixed-Scale StatisticsFixed-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:
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:
ResultsResults
Raw exit timesRaw exit times
R = 815 = 1.05R = 815 = 1.05
New J. Phys. 8:109, 2006New J. Phys. 8:109, 2006
ResultsResults
Raw exit timesRaw exit times
Subtracted exit timesSubtracted exit times
New J. Phys. 8:109, 2006New J. Phys. 8:109, 2006
Richardson Constant?Richardson Constant?
Raw exit timesRaw exit times
Subtracted exit timesSubtracted exit times
New J. Phys. 8:109, 2006New J. Phys. 8:109, 2006
ConclusionsConclusions 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?
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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