Elastic turbulence in a shell model of polymer solution

Ray, Samriddhi Sankar; Vincenzi, Dario

doi:10.1209/0295-5075/114/44001

Cited by 53 publications

(2 citation statements)

References 50 publications

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“…One, the scale-dependent Reynolds number in the elastic range is not necessarily very small. Two, we find ξ ≈ 2.3, whereas almost all studies of elastic turbulence find ξ > 3 ( 18 , 23 , 35 , 36 , 58 , 59 ), consistent with the theory of Fouxon and Lebedev ( 14 ). Note that at least one other simulation of elastic turbulence ( 60 ) has found ξ < 3 in two dimensional polymeric flows.…”

Section: Discussionsupporting

confidence: 86%

Large is different: Nonmonotonic behavior of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers

2023

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We use direct numerical simulations to study homogeneous and isotropic turbulent flows of dilute polymer solutions at high Reynolds and Deborah numbers. We find that for small wave numbers k , the kinetic energy spectrum shows Kolmogorov-like behavior that crosses over at a larger k to a novel, elastic scaling regime, E ( k ) ∼ k −ξ , with ξ ≈ 2.3. We study the contribution of the polymers to the flux of kinetic energy through scales and find that it can be decomposed into two parts: one increase in effective viscous dissipation and a purely elastic contribution that dominates over the nonlinear flux in the range of k over which the elastic scaling is observed. The multiscale balance between the two fluxes determines the crossover wave number that depends nonmonotically on the Deborah number. Consistently, structure functions also show two scaling ranges, with intermittency present in both of them in equal measure.

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Section: Discussionsupporting

confidence: 86%

Large is different: Nonmonotonic behavior of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers

2023

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“…Earlier theoretical arguments 37 have suggested ξ > 3, which has also been observed in experiments 42 – 44 – ξ ≈ 3.5 over less than a decade of scaling range. We obtain ξ ≈ 4, which satisfies the inequality and agrees with shell-model simulations 45 . Earlier theoretical arguments 37 , 46 had also assumed the same balance in the momentum equation that we have, but in addition, had assumed scale separation and a large-scale alignment of polymers in analogy with magnetohydrodynamics, obtaining ξ = χ + 2, which is not satisfied by our DNS.…”

Section: Resultssupporting

confidence: 87%

Intermittency in the not-so-smooth elastic turbulence

Singh,

Perlekar,

Mitra

et al. 2024

Nat Commun

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Elastic turbulence is the chaotic fluid motion resulting from elastic instabilities due to the addition of polymers in small concentrations at very small Reynolds ($${{{{{{{\rm{Re}}}}}}}}$$ Re ) numbers. Our direct numerical simulations show that elastic turbulence, though a low $${{{{{{{\rm{Re}}}}}}}}$$ Re phenomenon, has more in common with classical, Newtonian turbulence than previously thought. In particular, we find power-law spectra for kinetic energy E(k) ~ k−4 and polymeric energy Ep(k) ~ k−3/2, independent of the Deborah (De) number. This is further supported by calculation of scale-by-scale energy budget which shows a balance between the viscous term and the polymeric term in the momentum equation. In real space, as expected, the velocity field is smooth, i.e., the velocity difference across a length scale r, δu ~ r but, crucially, with a non-trivial sub-leading contribution r3/2 which we extract by using the second difference of velocity. The structure functions of second difference of velocity up to order 6 show clear evidence of intermittency/multifractality. We provide additional evidence in support of this intermittent nature by calculating moments of rate of dissipation of kinetic energy averaged over a ball of radius r, εr, from which we compute the multifractal spectrum.

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Research on viscoelastic fluid unsteady flow model based on torque loss correction

Liu

Liu³

et al. 2021

Polymer Testing

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Elastic turbulence in a shell model of polymer solution

Cited by 53 publications

References 50 publications

Large is different: Nonmonotonic behavior of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers

Large is different: Nonmonotonic behavior of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers

Intermittency in the not-so-smooth elastic turbulence

Research on viscoelastic fluid unsteady flow model based on torque loss correction

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