Tetrahedron deformation and alignment of perceived vorticity and strain in a turbulent flow

Pumir, Alain; Bodenschatz, Eberhard; Xu, Haitao

doi:10.1063/1.4795547

Cited by 39 publications

(58 citation statements)

References 52 publications

(107 reference statements)

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“…This approach was introduced in the framework of Lagrangian turbulence (in that case, the points are fluid particles), and allowed to investigate the structure of isotropic turbulence at different scales. 18,[32][33][34] We perform here Eulerian measurements, by considering sets of four points equally spaced in the flow to construct a perceived velocity gradient tensor, a procedure already used in a different context in rotating turbulence. 28 Several distances r 0 between the points, ranging from ≈η to ≈L/ √ 2, were considered, so as to cover the entire inertial range.…”

Section: Multiscale Analysis In Forced Turbulencementioning

confidence: 99%

“…In homogeneous and isotropic turbulence (HIT), for instance, the alignment properties of vorticity with the strain eigenvectors or, equivalently, with the vortex stretching vector, turned out to be one of the rare quantitative statistical manifestations of the existence of internal organization in the flow 16,17 (an analysis that can be extended at various scales, see, e.g., Ref. 18). The nonlinearity depletion phenomenon, another important feature of turbulence occurring at high Reynolds numbers, both in HIT 19,20 and in more realistic flows, 21 can also be evidenced by investigating the velocity and vorticity vectors relative orientation.…”

Section: Introductionmentioning

confidence: 99%

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Cyclone-anticyclone asymmetry and alignment statistics in homogeneous rotating turbulence

Naso

2015

Physics of Fluids

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International audienceThe cyclone-anticyclone asymmetry occurring in rotating turbulence is investigated through the analysis of the alignment statistics between vorticity and the rotation vector. The advantage of this approach, as compared to the usual measurement of the vertical vorticity skewness, is that the symmetry-breaking can be thus quantified through the analysis of first- and second-order moments, whose statistics convergence is more easily achieved than that of third-order ones. The vorticity/rotation alignment statistics are investigated by direct numerical simulation, both in forced and in freely decaying homogeneous turbulence. In the forced case, the cyclone-anticyclone asymmetry gets stronger as the Rossby number is decreased, whereas the opposite behavior occurs in the decaying case. These findings are shown to be consistent with the existence of a non-monotonic Rossby-number dependence of the asymmetry. A preferential antialignment of vorticity with the rotation vector is found in all the flows considered, a behavior supported by geometrical arguments and by a Taylor expansion of the Navier-Stokes equations for early times of rotation and in the weak rotation limit. A multiscale analysis of the alignment properties between vorticity and the rotation vector is also carried out in the forced case, evidencing the existence of a scale at which both the symmetry-breaking and the collinearity between the two vectors are maxima

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Section: Multiscale Analysis In Forced Turbulencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cyclone-anticyclone asymmetry and alignment statistics in homogeneous rotating turbulence

Naso

2015

Physics of Fluids

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“…Similar methods employing the advection of a tessellation of test particles can be used in simulations of incompressible flows, allowing the calculation of Lagrangian flow properties (e.g. Pumir et al 2013). …”

Section: Projections Of Phase Space In N -Body Simulations and The Damentioning

confidence: 99%

The properties of cosmic velocity fields

Hahn¹,

Angulo²,

Abel³

2015

Mon. Not. R. Astron. Soc.

122

170

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Understanding the velocity field is very important for modern cosmology: it gives insights to structure formation in general, and also its properties are crucial ingredients in modelling redshift-space distortions and in interpreting measurements of the kinetic Sunyaev-Zeldovich effect. Unfortunately, characterising the velocity field in cosmological N -body simulations is inherently complicated by two facts: i) The velocity field becomes manifestly multi-valued after shell-crossing and has discontinuities at caustics. This is due to the collisionless nature of dark matter. ii) N -body simulations sample the velocity field only at a set of discrete locations, with poor resolution in low-density regions. In this paper, we discuss how the associated problems can be circumvented by using a phase-space interpolation technique. This method provides extremely accurate estimates of the cosmic velocity fields and its derivatives, which can be properly defined without the need of the arbitrary "coarse-graining" procedure commonly used. We explore in detail the configuration-space properties of the cosmic velocity field on very large scales and in the highly nonlinear regime. In particular, we characterise the divergence and curl of the velocity field, present their one-point statistics, analyse the Fourier-space properties and provide fitting formulae for the velocity divergence bias relative to the non-linear matter power spectrum. We furthermore contrast some of the interesting differences in the velocity fields of warm and cold dark matter models. We anticipate that the high-precision measurements carried out here will help to understand in detail the dynamics of dark matter and the structures it forms.

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“…Their relative position and velocity with respect to the center of mass of the particle cloud are x ′n (t) = x n (t) − n x n (t)/N and u ′n (t) = u n (t) − n u n (t)/N , respectively. Determining the velocity gradient tensor A ij can then be formulated as a least-squares problem by finding the minimum value of the squared residuals S = n [u ′n i (t) − A ij x ′n j (t)] 2 (Pumir et al 2013). In general, however, the tracer particles in the cloud surrounding a rod are randomly distributed in space, and will sometimes lie in almost in the same plane.…”

Section: Seeding Density and Shape Factormentioning

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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Tetrahedron deformation and alignment of perceived vorticity and strain in a turbulent flow

Cited by 39 publications

References 52 publications

Cyclone-anticyclone asymmetry and alignment statistics in homogeneous rotating turbulence

Cyclone-anticyclone asymmetry and alignment statistics in homogeneous rotating turbulence

The properties of cosmic velocity fields

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

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