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

Gustavsson, K.; Mehlig, B.

doi:10.1007/s10955-013-0848-z

Cited by 9 publications

(18 citation statements)

References 38 publications

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“…[22], in which an increase of the compressibility factor C was associated with an important upscale energy transfer, we find that compressibility is larger for larger Rer , when the upscale energy transfer is proportionally stronger. We also remark that a compressibility factor larger than the critical value C = 0.5 is of significant importance: it suggests the occurrence of extreme events (velocity sources and sinks, 033010-5 associated to pointlike structures), which might have strong influence on the dispersion of chemical species and particles in free-surface flows [1] but also in other flow instances [23],…”

Section: B Flow Topology and Energy Cascadementioning

confidence: 89%

Upscale energy transfer and flow topology in free-surface turbulence

2015

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Free-surface turbulence, albeit constrained onto a two-dimensional space, exhibits features that barely resemble predictions of simplified two-dimensional modeling. We demonstrate that, in a three-dimensional open channel flow, surface turbulence is characterized by upscale energy transfer, which controls the long-term evolution of the larger scales. We are able to associate downscale and upscale energy transfer at the surface with the two-dimensional divergence of velocity. We finally demonstrate that surface compressibility confirms the strongly three-dimensional nature of surface turbulence.

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Section: B Flow Topology and Energy Cascadementioning

confidence: 89%

Upscale energy transfer and flow topology in free-surface turbulence

2015

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“…But the effect is weak; it occurs to order Ku 6 . Equation (6) (extended to order Ku 8 ) can be resummed by Padé-Borel resummation [22], yielding accurate results up to Ku ∼ 1.…”

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confidence: 99%

Tumbling of Small Axisymmetric Particles in Random and Turbulent Flows

2014

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We analyze the tumbling of small nonspherical, axisymmetric particles in random and turbulent flows. We compute the orientational dynamics in terms of a perturbation expansion in the Kubo number, and obtain the tumbling rate in terms of Lagrangian correlation functions. These capture preferential sampling of the fluid gradients, which in turn can give rise to differences in the tumbling rates of disks and rods. We show that this is a weak effect in Gaussian random flows. But in turbulent flows persistent regions of high vorticity cause disks to tumble much faster than rods, as observed in direct numerical simulations [S. Parsa, E. Calzavarini, F. Toschi, and G. A. Voth, Phys. Rev. Lett. 109, 134501 (2012)]. For larger particles (at finite Stokes numbers), rotational and translational inertia affects the tumbling rate and the angle at which particles collide, due to the formation of rotational caustics.

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“…At the compressibility ℘ = 1, the point clouds condense into a single point whose location depends on the Kubo number. The reason is that conditions (13) constrain the velocity gradients into the form…”

Section: Results and Special Casesmentioning

confidence: 99%

“…This relation follows the definition used in article [13]: there K = u 0 T /η with u 0 being the typical speed of the flow and η being its correlation length. By using Eq.…”

Section: The Model and Methodsmentioning

confidence: 97%

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On the effect of finite-time correlations on the turbulent mixing in smooth chaotic compressible velocity fields

Ainsaar¹,

Kalda²

2015

Proc. Estonian Acad. Sci.

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Most theoretical results about turbulent mixing have been obtained for ideal flows that are delta-correlated in time. As is often believed, those ideal flows are, with regard to mixing, very similar to real flows with a finite correlation time. However, recent results show that these two cases may differ considerably. In this article we study the effects of finite correlation time in a chaotic smooth statistically isotropic two-dimensional velocity field. As mixing is predominantly determined by the statistics of the stretching of material elements (e.g. lines "painted" onto a liquid), in this article we focus on the characteristics describing such stretching: finite-time Lyapunov exponents and the Lyapunov dimension. For these quantities, we derive analytical expressions as functions of the correlation time and the compressibility of the velocity field, and we investigate these expressions numerically. The results agree well with numerical results of other authors, and are useful for understanding several physical phenomena, e.g. patchiness of pollution spreading on an ocean and kinematic magnetic dynamos.

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

Cited by 9 publications

References 38 publications

Upscale energy transfer and flow topology in free-surface turbulence

Upscale energy transfer and flow topology in free-surface turbulence

Tumbling of Small Axisymmetric Particles in Random and Turbulent Flows

On the effect of finite-time correlations on the turbulent mixing in smooth chaotic compressible velocity fields

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