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?