A quantitative study of three-dimensional Lagrangian particle tracking algorithms

Ouellette, Nicholas T.; Xu, Haitao; Bodenschatz, Eberhard

doi:10.1007/s00348-005-0068-7

Cited by 423 publications

(429 citation statements)

References 24 publications

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“…The swimming speed, V C , of each cell was drawn from a probability distribution obtained from H. akashiwo cells swimming within the central plane of the experimental device in the absence of flow. Cell trajectories were obtained from movies recorded at 20 Hz using automated software (PredictiveTracker; Ouellette et al 42 ). To estimate the threedimensional swimming velocity from its measured (x Ã , z Ã ) projection, we assumed isotropy in x Ã and y Ã to obtain V C ¼ (2v x Ã2 þ v z…”

Section: Methodsmentioning

confidence: 99%

Turbulence drives microscale patches of motile phytoplankton

et al. 2013

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Patchiness plays a fundamental role in phytoplankton ecology by dictating the rate at which individual cells encounter each other and their predators. The distribution of motile phytoplankton species is often considerably more patchy than that of non-motile species at submetre length scales, yet the mechanism generating this patchiness has remained unknown. Here we show that strong patchiness at small scales occurs when motile phytoplankton are exposed to turbulent flow. We demonstrate experimentally that Heterosigma akashiwo forms striking patches within individual vortices and prove with a mathematical model that this patchiness results from the coupling between motility and shear. When implemented within a direct numerical simulation of turbulence, the model reveals that cell motility can prevail over turbulent dispersion to create strong fractal patchiness, where local phytoplankton concentrations are increased more than 10-fold. This 'unmixing' mechanism likely enhances ecological interactions in the plankton and offers mechanistic insights into how turbulence intensity impacts ecosystem productivity.

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Section: Methodsmentioning

confidence: 99%

Turbulence drives microscale patches of motile phytoplankton

et al. 2013

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“…The third camera was aimed up toward the same volume at an angle of 21 • . Situating the three cameras in different planes helps to increase the stereomatching accuracy (Ouellette et al 2006).…”

Section: Scanning Systemmentioning

confidence: 99%

“…This procedure is used for both types of particles. From the two-dimensional (2D) positions of the particles as measured by each camera, the three-dimensional (3D) positions can be found by stereoscopic matching, and subsequently connected together in time from one volume scan to the next (Ouellette et al 2006), although some modifications of common tracking algorithms are required.…”

Section: Particle Trackingmentioning

confidence: 99%

“…To handle this ambiguity, we first track the particles found in each individual slab separately, and then subsequently merge the short segments that belong to different slabs but that refer to the same particle. Within each slab, particles are tracked using a standard predictive tracking algorithm (Ouellette et al 2006), with a recording time of roughly ∼ d/∆tũ = 75 frames, where d = 3 mm andũ ∼ 2 cm/s are the thickness of one laser slab and the root-mean-square velocity of the flow, respectively. In figure 6(b), it is seen that each pair of neighboring slabs overlaps by d ov ∼ 1.5 mm.…”

Section: Particle Trackingmentioning

confidence: 99%

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Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence

Kramel

Ouellette

et al. 2015

J. Fluid Mech.

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We present simultaneous experimental measurements of the dynamics of anisotropic particles transported by a turbulent flow and the velocity gradient tensor of the flow surrounding them. We track both rod-shaped particles and small spherical flow tracers using stereoscopic particle tracking. By using scanned illumination, we are able to obtain a high enough seeding density of tracers to measure the full velocity gradient tensor near the rod. The alignment of rods with the vorticity and the eigenvectors of the strain rate show agreement with numerical simulations. A full description of the tumbling of rods in turbulence requires specifying a seven-dimensional joint probability density function (PDF) of five scalars characterizing the velocity gradient tensor and two scalars describing the relative orientation of the rod. If these seven parameters are known, then Jeffery's equation specifies the rod tumbling rate and any statistic of rod rotations can be obtained as a weighted average over the joint PDF. To look for a lower-dimensional projection to simplify the problem, we explore conditional averages of the mean-squared tumbling rate. The conditional dependence of the mean-squared tumbling rate on the magnitude of both the vorticity and the strain rate is strong, as expected, and similar. There is also a strong dependence on the orientation between the rod and the vorticity, since a rod aligned with the vorticity vector tumbles due to strain but not vorticity. When conditioned on the alignment of the rod with the eigenvectors of the strain rate, the largest tumbling rate is obtained when the rod is oriented at a certain angle to the eigenvector that corresponds to the smallest eigenvalue, because this particular orientation maximizes the contribution from both the vorticity and strain.

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“…When we run d.c. electric current (up to 1 A) through the salt water, Lorentz forces produce motion that lies almost entirely in the plane 13,[18][19][20][21] . We measure the fluid motion by tracking 22 51 µm polystyrene particles using a 4 megapixel digital camera at 60 frames per second. The particles are small enough to follow the flow accurately 21 and lie at the interface between the salt water and a less dense pure water layer, eliminating surface-tension-driven interactions between the particles 23 .…”

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confidence: 99%

Separating stretching from folding in fluid mixing

Kelley

Ouellette

2011

Nature Phys

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Fluid mixing controls many natural and industrial processes, including the spread of air pollution 1 , mass transfer and reactions in microfluidic devices 2,3 and the detection of odours or other chemical signals 4 . Strongly nonlinear flows enhance mixing by chaotic advection 5,6 , stretching and folding 7,8 fluid volumes. Though these processes have been studied in simple models 9,10 , stretching and folding are difficult to distinguish in real flows with complex spatiotemporal structure. Here we report measurements of these two distinct processes in a two-dimensional laboratory flow. We decouple stretching and folding using tools developed for analysing glassy solids 11 and colloids 12 , breaking fluid deformation into a linear, affine component (primarily stretching) and a nonlinear, non-affine component (primarily folding). Short-time deformation is dominated by stretching, whereas folding occurs only after fluid elements are elongated. The relative strength of the two processes depends strongly on space and time; foldingdominated regions are initially isolated, but later grow to fill space.Mixing is fundamentally a diffusion process: at the boundary of an impurity in a fluid, the concentration gradient is large and material flows until the gradient vanishes. Diffusion alone is inefficient for large-scale transport, such as is required in industrial mixers or observed in geophysical flow. Moving fluids, however, can greatly enhance mixing through chaotic advection 5,6 . As the fluid moves, the region containing the impurity is strongly deformed, the length of its boundary grows exponentially and diffusion becomes efficient. The key to understanding chaotic mixing, then, is the characterization of the deformation of fluid elements 8 . As first described by Reynolds 7 , this process is one of stretching, which increases the length of the interface, and folding, which constrains the fluid element to fill a finite region of space. These geometric processes are often studied in simple mathematical models such as the baker's or horseshoe maps 9,10 . Such models, however, differ from actual fluid flow in that they are discrete, periodic and highly idealized. Although stretching and folding have been described qualitatively in real flows 2,13,14 , they have not been quantitatively distinguished spatially, temporally or dynamically in flows with complex spatiotemporal structure.Deformation of a material volume consists of the relative motion, and potentially rearrangement, of infinitesimal fluid elements. These relative displacements can be broadly characterized as either affine-that is, some combination of rotation, shear, dilation or compression 15 -or non-affine. Affine deformation is linear, and can be represented by a matrix operator. Non-affine deformation is nonlinear, and generally consists of irreversible rearrangements of the constituent volume elements 11 . This distinction between affine and non-affine deformation has been used to study shear transformation zones and plasticity in metallic glasses 11,16 ...

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A quantitative study of three-dimensional Lagrangian particle tracking algorithms

Cited by 423 publications

References 24 publications

Turbulence drives microscale patches of motile phytoplankton

Turbulence drives microscale patches of motile phytoplankton

Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence

Separating stretching from folding in fluid mixing

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