Comparison of Lagrangian and Eulerian frames of passive scalar turbulent mixing

Götzfried, Paul; Emran, Mohammad S.; Villermaux, Emmanuel; Schumacher, Jörg

doi:10.1103/physrevfluids.4.044607

Cited by 12 publications

(7 citation statements)

References 46 publications

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“…But one can do better in terms of the quality of scaling by restricting attention on cliff regions connected to a persistent local straining motion, a known process studied in the chaotic mixing regime of high-Schmidt-number turbulence [27][28][29]. For this purpose, we refine the analysis and examine strain-dominated subsets in the cliff regions.…”

Section: Unique Monofractal Scaling In Strain-dominated Cliff Regionsmentioning

confidence: 99%

Fractal iso-level sets in high-Reynolds-number scalar turbulence

et al. 2020

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We study the fractal scaling of iso-levels sets of a passive scalar mixed by three-dimensional homogeneous and isotropic turbulence at high Reynolds numbers. The Schmidt number is unity. A fractal box-counting dimension DF can be obtained for iso-levels below about 3 standard deviations of the scalar fluctuation on either side of its mean value. The dimension varies systematically with the iso-level, with a maximum of about 8/3 for the iso-level at the mean; this maximum dimension also follows as an upper bound from the geometric measure theory. We interpret this result to mean that mixing in turbulence is always incomplete. A unique box-counting dimension for all iso-levels results when we consider the spatial support of the steep cliffs of the scalar conditioned on local strain; that unique dimension is about 4/3. *

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Section: Unique Monofractal Scaling In Strain-dominated Cliff Regionsmentioning

confidence: 99%

Fractal iso-level sets in high-Reynolds-number scalar turbulence

et al. 2020

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“…On one hand, Lagrangian methods consisting in following particles along their trajectory in the flow (Yeung 2002) do not consider the diffusion of the scalar. Brownian motion (Öttinger 1996) can be added to represent diffusion but it requires an enormous number of tracers that can be extremely costly (Götzfried et al 2019). On the other hand, Eulerian methods cannot deal with weakly diffusing species in multiscale flows at high Reynolds and Schmidt numbers (Yeung, Donzis & Sreenivasan 2005;Schwertfirm & Manhart 2007) because of the refined resolution (spatial grid in particular) capabilities it requires.…”

Section: Introductionmentioning

confidence: 99%

The diffuselet concept for scalar mixing

Meunier

Villermaux

2022

J. Fluid Mech.

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The advection–diffusion of a small surface element of scalar in three dimensions (or of a small line element in two dimensions) is solved analytically thanks to the Ranz transform (Ranz, AIChE J., vol. 25, issue 1, 1979, pp. 41–47). As the quantum or elementary brick of any complex mixture, we call this element a diffuselet. Its evolution is computed numerically from the integration of the velocity gradient along the trajectory, as classically done for the Lyapunov exponents. The concentration profile across the diffuselet is obtained from the product of its initial orientation with a dimensionless tensor. Averaging over all initial orientations yields simple formulae for the mean scalar variance and the scalar probability distribution function (p.d.f.). This technique is then applied to two-dimensional and three-dimensional sine flows, in excellent agreement with direct numerical simulations. For these simple flows, the temporal integration is obtained analytically leading to simple integrals for the scalar variance and p.d.f. Statistics of stretching rates are calculated as well. The Lyapunov exponent is close to the value for short-time correlated flows (Kraichnan, J. Fluid Mech., vol. 64, issue 4, 1974, pp. 737–762) in the case of a small displacement during each step; it is close to the value for a simple shear in the case of a large displacement. The p.d.f. of stretching factors are log normal with a ratio between the mean and the variance equal to half the dimension of space for small displacements (in agreement with Kraichnan, J. Fluid Mech., vol. 64, issue 4, 1974, pp. 737–762), but increases strongly for large displacements.

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“…of local concentration has been discussed by Götzfried et al. (2019), demonstrating the relevance of FTLE for the organization of concentration in sheets. The width of these sheets has been related to the distribution of FTLE (Kushnir, Schumacher & Brandt 2006).…”

Section: Introductionmentioning

confidence: 81%

Do coherent structures organize scalar mixing in a turbulent boundary layer?

2021

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A scalar emanating from a point source in a turbulent boundary layer does not mix homogeneously, but is organized in large regions with little variation of the concentration: uniform concentration zones. We measure scalar concentration using laser-induced fluorescence and, simultaneously, the three-dimensional velocity field using tomographic particle image velocimetry in a water tunnel boundary layer. We identify uniform concentration zones using both a simple histogram technique, and more advanced cluster analysis. From the complete information on the turbulent velocity field, we compute two candidate velocity structures that may form the boundaries between two uniform concentration zones. One of these structures is related to the rate of point separation along Lagrangian trajectories and the other one involves the magnitude of strong shear in snapshots of the velocity field. Therefore, the first method allows for the history of the flow field to be monitored, while the second method only looks at a snapshot. The separation of fluid parcels in time was measured in two ways: the exponential growth of the separation as time progresses (related to finite-time Lyapunov exponents and unstable manifolds in the theory of dynamical systems), and the exponential growth as time moves backward (stable manifolds). Of these two, a correlation with the edges of uniform concentration zones was found for the past Lyapunov field but not with the time-forward future field. The magnitude of the correlation is comparable to that of the regions of strong shear in the instantaneous velocity field.

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Comparison of Lagrangian and Eulerian frames of passive scalar turbulent mixing

Cited by 12 publications

References 46 publications

Fractal iso-level sets in high-Reynolds-number scalar turbulence

Fractal iso-level sets in high-Reynolds-number scalar turbulence

The diffuselet concept for scalar mixing

Do coherent structures organize scalar mixing in a turbulent boundary layer?

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