Tumbling of Small Axisymmetric Particles in Random and Turbulent Flows

Gustavsson, K.; Einarsson, Jonas; Mehlig, B.

doi:10.1103/physrevlett.112.014501

Cited by 80 publications

(95 citation statements)

References 34 publications

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“…Second, a related Ku-expansion was recently used to compute the tumbling rate of small axisymmetric particles in three-dimensional random velocity fields at finite Kubo numbers [37]. It turns out that the resummation works well also for the series expansion of the tumbling rate.…”

Section: Discussionmentioning

confidence: 99%

Lyapunov Exponents for Particles Advected in Compressible Random Velocity Fields at Small and Large Kubo Numbers

Gustavsson

Mehlig

2013

J Stat Phys

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We calculate the Lyapunov exponents describing spatial clustering of particles advected in one-and two-dimensional random velocity fields at finite Kubo numbers Ku (a dimensionless parameter characterising the correlation time of the velocity field). In one dimension we obtain accurate results up to Ku ∼ 1 by resummation of a perturbation expansion in Ku. At large Kubo numbers we compute the Lyapunov exponent by taking into account the fact that the particles follow the minima of the potential function corresponding to the velocity field. The Lyapunov exponent is always negative. In two spatial dimensions the sign of the maximal Lyapunov exponent λ 1 may change, depending upon the degree of compressibility of the flow and the Kubo number. For small Kubo numbers we compute the first four non-vanishing terms in the small-Ku expansion of the Lyapunov exponents. By resumming these expansions we obtain a precise estimate of the location of the path-coalescence transition (where λ 1 changes sign) for Kubo numbers up to approximately Ku = 0.5. For large Kubo numbers we estimate the Lyapunov exponents for a partially compressible velocity field by assuming that the particles sample those stagnation points of the velocity field that have a negative real part of the maximal eigenvalue of the matrix of flow-velocity gradients.

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Section: Discussionmentioning

confidence: 99%

Lyapunov Exponents for Particles Advected in Compressible Random Velocity Fields at Small and Large Kubo Numbers

Gustavsson

Mehlig

2013

J Stat Phys

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“…From numerical simulations (Pumir & Wilkinson 2011;Gustavsson et al 2014) we know the probability distributions of the projection ofp onto the vorticity and the eigenvectors of the strain rate. But predicting the tumbling rate requires the full joint probability distribution of the velocity gradient tensor and the particle orientation.…”

Section: Introductionmentioning

confidence: 99%

“…Chevillard & Meneveau (2013) studied the full parameter space of tri-axial ellipsoids in numerical simulations and showed that the tumbling of rods is a challenging test case for stochastic models of the velocity gradient tensor in turbulence. Gustavsson et al (2014) used analytical and numerical methods to show the differences in tumbling between rods and disks can be understood using Lagrangian three-point correlations of the velocity gradient tensor. Parsa & Voth (2014) made experimental measurements of the rotation of rods with lengths extending into the inertial range of turbulence and proposed that rotations of long rods should show inertial range scaling.…”

Section: Introductionmentioning

confidence: 99%

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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“…The dynamics of inertia-free spheroidal particles in homogeneous isotropic turbulence has been subject to several numerical studies [1][2][3][4][5][6] and also a few experimental investigations. [7][8][9] It has been observed that disk-like particles tumble more than rod-like particles.…”

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confidence: 99%

Shape effects on dynamics of inertia-free spheroids in wall turbulence

2015

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The rotational motion of inertia-free spheroids has been studied in a numerically simulated turbulent channel flow. Although inertia-free spheroids were translated as tracers with the flow, neither the disk-like nor the rod-like particles adapted to the fluid rotation. The flattest disks preferentially aligned their symmetry axes normal to the wall, whereas the longest rods were parallel with the wall. The shape-dependence of the particle orientations carried over to the particle rotation such that the mean spin was reduced with increasing departure from sphericity. The streamwise spin fluctuations were enhanced due to asphericity, but substantially more for prolate than for oblate spheroids.

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Tumbling of Small Axisymmetric Particles in Random and Turbulent Flows

Cited by 80 publications

References 34 publications

Lyapunov Exponents for Particles Advected in Compressible Random Velocity Fields at Small and Large Kubo Numbers

Lyapunov Exponents for Particles Advected in Compressible Random Velocity Fields at Small and Large Kubo Numbers

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

Shape effects on dynamics of inertia-free spheroids in wall turbulence

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