The Role of Pair Dispersion in Turbulent Flow

Bourgoin, Mickaël; Ouellette, Nicholas T.; Xu, Haitao; Berg, Jacob; Bodenschatz, Eberhard

doi:10.1126/science.1121726

Cited by 200 publications

(213 citation statements)

References 27 publications

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“…The original formula proposed by Richardson (1926), D 2 (t) = Ctt\ where C = 0(1) is a constant and f is the turbulent kinetic energy dissipation rate, is found to be consistent with Kolmogorov's (1941) energy-cascade law for three-dimensional (3D), homogeneous, isotropic turbulence in the inertial range, E(k) ~ e 2/3 Jt _5/5 (Batchelor, 1952). Nevertheless, the precise mechanisms responsible for Richardson's (1926) relation and the range of conditions under which it is valid remains the subject of some debate even in idealized experimental and numerical settings (e.g., Bourgoin et al, 2006). The direct applicability to oceanic flows, which tend to be two-dimensional (2D) under the effects of rotation and stratification (Cushman-Roisin, 1995) and which are often dominated by persistent inhomogeneity and anisotropy, is open to question.…”

Section: (3)mentioning

confidence: 72%

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Relative dispersion from a high-resolution coastal model of the Adriatic Sea

et al. 2008

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Section: (3)mentioning

confidence: 72%

“…Bourgoin et al (2006) obtained Batchelor (1952) scaling (similar to ballistic) in 3D homogeneous turbulence in the laboratory, but could not confirm the Richardson regime. Numerical simulations of 2D homogeneous turbulence Bracco ct al., 2004) yielded both the exponential and Richardson regimes.…”

Section: (3)mentioning

confidence: 99%

Relative dispersion from a high-resolution coastal model of the Adriatic Sea

et al. 2008

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“…This finding was again questioned, though, in Ref. 15. Generally, experiments, both numerical and real, are still limited to flows with low Reynolds numbers.…”

Section: Introductionmentioning

confidence: 91%

“…Kinematic simulations ͑KS͒ of turbulent-like flows [7][8][9] offers the possibility to study a number of dispersion aspects, also at high Reynolds numbers. Only recently [10][11][12][13][14][15] has it become possible to study the second moment of the probability density function ͑PDF͒ of the separation r͑t͒ between two particles also in real turbulence via direct numerical simulation ͑DNS͒ or experiment, with the notable exception of Bourgoin et al 15 at typically low to intermediate Reynolds numbers. Relative dispersion of fluid particles still serves as a benchmark problem for our current understanding of turbulence.…”

Section: Introductionmentioning

confidence: 99%

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Self Similar Two Particle Separation Model

Lüthi¹,

Berg²,

Ott³

et al.

Springer Proceedings in Physics

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We present a new stochastic model for relative two-particle separation in turbulence. Inspired by material line stretching, we suggest that a similar process also occurs beyond the viscous range, with time scaling according to the longitudinal second-order structure function S 2 ͑r͒, e.g.; in the inertial range as −1/3 r 2/3 . Particle separation is modeled as a Gaussian process without invoking information of Eulerian acceleration statistics or of precise shapes of Eulerian velocity distribution functions. The time scale is a function of S 2 ͑r͒ and thus of the Lagrangian evolving separation. The model predictions agree with numerical and experimental results for various initial particle separations. We present model results for fixed time and fixed scale statistics. We find that for the Richardson-Obukhov law, i.e., ͗r͑t͒ 2 ͘ = g t 3 , to hold and to also be observed in experiments, high Reynolds numbers are necessary, i.e., Re Ͼ O͑1000͒, and the integral scale needs to be large compared to initial separation, i.e., L / r 0 Ͼ 30 and d / L Ͼ 3 need to be fulfilled, where d is the size of the field of view. Removing the constraint of finite inertial range, the model is used to explore separation dynamics in the asymptotic regime. As Re → ϱ, the distance neighbor function takes on a constant shape, almost as predicted by the Richardson diffusion equation. For the Richardson constant we obtain that g → 0.95 as Re → ϱ. This asymptotic limit is reached at Re Ͼ 1000. For the Richardson constant g, the model predicts a ratio of g b / g f Ϸ 1.9 between backwards and forwards dispersion.

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Lagrangian Methods in Experimental Fluid Mechanics

Bourgoin¹,

Pinton²,

Volk³

2014

Modeling Atmospheric and Oceanic Flows

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Experimental techniques yielding measurement with high resolution in time and space domains have had a large impact in fluid mechanics over the past ten years. This review concentrates on Lagrangian approaches since the understanding of the motions of fluid particles is critical for transport phenomena, which play a major role in geophysical fluid dynamics. Applications range from mixing problems, passive and active scalar advection, to dispersion of particles, accretion or fragmentation. Experimental methods have been developed using several strategies: direct optical imaging to record the trajectories of tracer particles; scattering techniques (optics or acoustics) to track particle velocities and also probe density and vorticity fluctuations in the flow; remote sensing techniques to record dynamics of tracers and objects passively advected by fluid motions. These methods, underlying principles and main results are discussed here.

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The Role of Pair Dispersion in Turbulent Flow

Cited by 200 publications

References 27 publications

Relative dispersion from a high-resolution coastal model of the Adriatic Sea

Relative dispersion from a high-resolution coastal model of the Adriatic Sea

Self Similar Two Particle Separation Model

Lagrangian Methods in Experimental Fluid Mechanics

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