Single Flow Snapshot Reveals the Future and the Past of Pairs of Particles in Turbulence

Falkovich, Gregory; Frishman, Anna

doi:10.1103/physrevlett.110.214502

Cited by 25 publications

(37 citation statements)

References 12 publications

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“…This was also confirmed by Sawford [13] and Borgas and Sawford [24]. However, the white noise assumption for the fluctuating pressure forces in a real turbulent flow situation, at finite Reynolds numbers, does not really seem to be justifiable, because real turbulent flows are spatially non-smooth but temporally finite-correlated (Falkovich and Frishman [25]). [R (t)]…”

Section: Application Of a Generalized Brownian Motion Modelsupporting

confidence: 50%

A generalized Brownian motion model for turbulent relative particle dispersion

Shivamoggi

2016

Physics Letters A

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In this paper, a generalized Brownian motion model has been applied to describe the relative particle dispersion problem in more realistic turbulent flows. The fluctuating pressure forces acting on a fluid particle are taken to be a colored noise and follow a stationary process and are described by the Uhlenbeck-Ornstein model while it appears plausible to take their correlation time to have a power-law dependence on the flow Reynolds number R e , thus introducing a bridge between the Lagrangian quantities and the Eulerian parameters for this problem. This ansatz is in qualitative agreement with the possibility of a connection speculated earlier by Corrsin [26] between the white-noise representation for the fluctuating pressure forces and the large-R e assumption in the Kolmogorov [4] theory for the 3D fully developed turbulence (FDT) as well as the argument of Monin and Yaglom [23] and the result of Sawford [13] and Borgas and Sawford [24] that the Lagrangian acceleration is deltafunction auto-correlated in the infinite-R e limit. It also provides an insight into the result that the Richardson-Obukhov scaling holds only in the infinite-R e limit and disappears otherwise. This ansatz further confirms the Lin-Reid [18] conjecture regarding the connection between the fluctuating pressure-force parameter and the energy dissipation rate in turbulence and leads to an R e -dependent explicit relation between the two speculated by Lin and Reid [18]. More specifically, this ansatz provides a determination of the Richardson-Obukhov constant g as a function of R e , with an asymptotic constant value in the infinite-R e limit. It is shown to lead to full agreement, in the small-R e limit as well, with the Batchelor-Townsend [27] scaling for the rate of change of the mean square interparticle separation in 3D FDT, hence validating its soundness further.

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Section: Application Of a Generalized Brownian Motion Modelsupporting

confidence: 50%

A generalized Brownian motion model for turbulent relative particle dispersion

Shivamoggi

2016

Physics Letters A

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“…That the energy flux-through-scale should appears in the Ott-Mann-Gawȩdzki relation (14) for Euler solutions was already essentially understood in [18,22]. Lemma 1 is a precise mathematical formulation of this observation.…”

Section: Introductionmentioning

confidence: 92%

“…It is now straightforward, following the approach of [2], to connected the anomaly (35) to dissipative properties of weak unforced Euler solutions under the assumption that u k f → u strongly in L 3 (0, T ; L 3 (T 2 )) provided that f k → 0 in the sense of distributions as k f → ∞ (for example, forcing given by Proposition 1). Then, it is easy to see that the limit u ∈ L 3 (0, T ; L 3 (T 2 )) is a weak solution to the unforced incompressible Euler equations (17)- (18) with f ≡ 0 which satisfies the local energy balance arising as the limit of Eq. (34)…”

Section: Anomalous Input In Dimension D =mentioning

confidence: 99%

Turbulent Cascade Direction and Lagrangian Time-Asymmetry

Drivas

2018

J Nonlinear Sci

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We establish Lagrangian formulae for energy conservation anomalies involving the discrepancy between short-time two-particle dispersion forward and backward in time. These results are facilitated by a rigorous version of the Ott-Mann-Gawȩdzki relation, sometimes described as a "Lagrangian analogue of the 4/5-law". In particular, we prove that for weak solutions of the Euler equations, the Lagrangian forward/backward dispersion measure matches on to the energy defect [1,2] in the sense of distributions. For strong limits of d ≥ 3 dimensional Navier-Stokes solutions the defect distribution coincides with the viscous dissipation anomaly. The Lagrangian formula shows that particles released into a 3d turbulent flow will initially disperse faster backward-in-time than forward, in agreement with recent theoretical predictions of Jucha et. al [3]. In two dimensions, we consider strong limits of solutions of the forced Euler equations with increasingly high-wavenumber forcing as a model of an ideal inverse cascade regime. We show that the same Lagrangian dispersion measure matches onto the anomalous input from the infinite-frequency force. As forcing typically acts as an energy source, this leads to the prediction that particles in 2d typically disperse faster forward in time than backward, which is opposite to what occurs in 3d. Time-asymmetry of the Lagrangian dispersion is thereby closely tied to the direction of the turbulent cascade, downscale in d ≥ 3 and upscale in d = 2. These conclusions lend support to the conjecture of [4] that a similar connection holds for time-asymmetry of Richardson two-particle dispersion and cascade direction, albeit at longer times.

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“…Although the pressure forces on average do not contribute to the kinetic energy balance, in three dimensions they are responsible for the redistribution of energy from slow to fast particles and for the asymmetry of the probability density function (PDF) of energy power. The absence of the analogous pressure forces in (2) suggests that the statistics of metenstrophy in the 2D direct cascade will be very different from the statistics of power in three dimensions.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Irreversibility of the two-dimensional enstrophy cascade

et al. 2016

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We study the time irreversibility of the direct cascade in two-dimensional turbulence by looking at the time derivative of the square vorticity along Lagrangian trajectories, a quantity called metenstrophy. By means of extensive direct numerical simulations we measure the time irreversibility from the asymmetry of the probability density function of the metenstrophy and we find that it increases with the Reynolds number of the cascade, similarly to what is found in three-dimensional turbulence. A detailed analysis of the different contributions to the enstrophy budget reveals a remarkable difference with respect to what is observed for the energy cascade, in particular the role of the statistics of the forcing to determine the degree of irreversibility.

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Single Flow Snapshot Reveals the Future and the Past of Pairs of Particles in Turbulence

Cited by 25 publications

References 12 publications

A generalized Brownian motion model for turbulent relative particle dispersion

A generalized Brownian motion model for turbulent relative particle dispersion

Turbulent Cascade Direction and Lagrangian Time-Asymmetry

Irreversibility of the two-dimensional enstrophy cascade

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