Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence

Briard, Antoine; Gomez, Thomas; Cambon, Claude

doi:10.1017/jfm.2016.362

Cited by 22 publications

(80 citation statements)

References 60 publications

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“…Basically, for Saffman turbulence α = −6/5 and for Batchelor turbulence α = −1.38. A similar extension was done recently for a passive scalar field [13,44] in Batchelor turbulence. These exponents for the velocity field are gathered in Table 2 and are referred to as Classical CBC exponents since they are valid in HIT.…”

Section: Decay Laws For K(t) and R 13 (T)mentioning

confidence: 61%

Decay and growth laws in homogeneous shear turbulence

Briard

Gomez²,

Mons

et al. 2016

Journal of Turbulence

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International audienceHomogeneous anisotropic turbulence has been widely studied in the past decades, both numerically and experimentally. Shear flows have received a particular attention because of the numerous physical phenomena they exhibit. In the present paper, both the decay and growth of anisotropy in homogeneous shear flows at high Reynolds numbers are revisited thanks to a recent eddy-damped quasi-normal Markovian (EDQNM) closure adapted to homogeneous anisotropic turbulence. The emphasis is put on several aspects: an asymptotic model for the slow-part of the pressure-strain tensor is derived for the return to isotropy process when mean-velocity gradients are released. Then, a general decay law for purely anisotropic quantities in Batchelor turbulence is proposed. At last, a discussion is proposed to explain the scattering of global quantities obtained in DNS and experiments in sustained shear flows: the emphasis is put on the exponential growth rate of the kinetic energy and on the shear parameter

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Section: Decay Laws For K(t) and R 13 (T)mentioning

confidence: 61%

Decay and growth laws in homogeneous shear turbulence

Briard

Gomez²,

Mons

et al. 2016

Journal of Turbulence

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“…Note that other anisotropic descriptors for scalar fields exist [19], and that for an isotropic state sin 2 γ = 2/3 unlike b 33 .…”

Section: -9mentioning

confidence: 99%

Harmonic to subharmonic transition of the Faraday instability in miscible fluids

2019

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When a stable stratification between two miscible fluids is excited by a vertical and periodic forcing, a turbulent mixing zone can develop, triggered by the Faraday instability. The mixing zone grows and saturates to a recently predicted final value L sat [Gréa and Ebo Adou, J. Fluid Mech. 837, 293 (2018)] when resonance conditions are no longer fulfilled. Notably, it is expected from the Mathieu stability diagram that the instability may evolve from a harmonic to a subharmonic regime for particular initial conditions. This transition is evidenced here in the full inhomogeneous system using direct numerical simulations with 1024 3 points: the analysis of one-point statistics and spectra reveals that turbulence is greatly enhanced after the transition, while the global anisotropy of both the velocity and concentration fields is significantly reduced. Furthermore, using the concept of sorted density field, we compute the background potential energy e b p of the flow, which increases only after the transition as a signature of irreversible mixing. While the gain in e b p strongly depends on the control parameters of the instability, the cumulative mixing efficiency is more robust. At saturation of the instability, available potential energy is partially released in the flow as background potential energy. Finally, it is shown numerically that for fixed parameters, a multiple-frequency forcing can modify the duration of the harmonic regime without significantly altering the asymptotic state.

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“…The numerical results obtained with such an approximation were thoroughly discussed in the previously mentioned references and compared quantitatively well with both DNS and experiments, in various configurations, from axisymmetric contractions, expansions, and plane distortions [1,3], to the transport of a passive scalar field in the presence of a mean gradient with a variable Prandtl number [2,14], along with the case of unstably stratified turbulence [4]. However, for shear flows, the model could not recover accurately the anisotropy distribution by investigating, for instance, several components of the global indicator b ij = u i u j /2K − δ ij /3, where K = ∞ 0 E(k) dk is the kinetic energy, nor the asymptotic value of the kinetic exponential growth rate γ as said earlier.…”

Section: Introductionmentioning

confidence: 87%

“…This expansion was further truncated at the second order for the sake of simplicity in [1]: the immediate drawback is the loss of angular anisotropic information which makes the production terms, linear with the mean-velocity gradient matrix A ln , not exact anymore. The consequences of such an approximation were thoroughly examined and discussed in several references [1][2][3], so that they are not further argued here. The aim of this study is precisely to improve the modelling of anisotropy through a truncation at the next even order, the fourth-one, in Section 3.…”

Section: The E-z Decompositionmentioning

confidence: 99%

“…In the past years, the authors have analysed separately each of these configurations with the help of an adapted eddy-damped quasi-normal Markovian (EDQNM) closure able of handling strongly anisotropic flows, in order to better understand what are the intrinsic properties of each mechanism. A significant amount of results, both theoretical and numerical, were exposed in various publications [1][2][3][4][5][6][7][8][9], and still a lot of work needs to be done regarding shear flows specifically. Indeed, the anisotropic EDQNM model developed in Mons, Cambon, and Sagaut (MCS) [1] handles very satisfactorily various straining processes, for instance when the mean-velocity gradient matrix is symmetric, like in axisymmetric contractions or expansions, or in plane distortions.…”

Section: Introductionmentioning

confidence: 99%

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Advanced spectral anisotropic modelling for shear flows

Briard

Gréa

Mons

et al. 2018

Journal of Turbulence

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0) ∼ k σ , unlike unstably stratified homogeneous turbulence where γ strongly depends on σ. The MCS model relies on the truncation at the second order of the spectral two-point velocity correlation expansion into spherical harmonics. The expansion is here pursued at the next even order, the fourth one: the noteworthy consequence is that γ is decreased compared to MCS and is thus closer to values obtained in direct numerical simulations and experiments. Finally, some analytical considerations about odd-order contributions in the expansion of polarisation anisotropy are proposed. In this work, the spectral modelling developed in MCS [Mons, Cambon, Sagaut. A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically-averaged descriptors. J Fluid Mech. 2016;788:147-182] for shear-driven turbulence is further analysed and then improved. First, using self-similarity arguments, it is shown that the asymptotic kinetic energy exponential growth rate γ is independent of the large scales infrared slope σ , with E(k →

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Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence

Cited by 22 publications

References 60 publications

Decay and growth laws in homogeneous shear turbulence

Decay and growth laws in homogeneous shear turbulence

Harmonic to subharmonic transition of the Faraday instability in miscible fluids

Advanced spectral anisotropic modelling for shear flows

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