Three-dimensional analysis of precursors to non-viscous dissipation in an experimental turbulent flow

Debue, Paul; Valori, Valentina; Cuvier, Christophe; Daviaud, François; Foucaut, Jean-Marc; Laval, Jean-Philippe; Wiertel, Cécile; Padilla, Vincent; Dubrulle, Bérengère

doi:10.1017/jfm.2020.574

Cited by 16 publications

(9 citation statements)

References 35 publications

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“…2015; Debue et al. 2021; Moffatt 2021). These local extreme viscous dissipation rates within the mixing regions are similar to fully developed turbulent flows, and they also decay with time.…”

Section: Resultsmentioning

confidence: 99%

Effect of chemical reaction on mixing transition and turbulent statistics of cylindrical Richtmyer–Meshkov instability

Yan

Wang

et al. 2022

J. Fluid Mech.

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Direct numerical simulations of a three-dimensional cylindrical Richtmyer–Meshkov instability with and without chemical reactions are carried out to explore the chemical reaction effects on the statistical characteristics of transition and turbulent mixing. We adopt 9-species and 19-reaction models of non-premixed hydrogen and oxygen separated by a multimode perturbed cylindrical interface. A new definition of mixing width suitable for a chemical reaction is introduced, and we investigate the spatio-temporal evolution of typical flow parameters within the mixing regions. After reshock with a fuller mixing of fuels and oxygen, the chemical reaction becomes sufficiently apparent at affecting the evolution of the flow fields. Because of the generation of a combustion wave within the combustion regions and propagation, the growth of the mixing width with a chemical reaction is accelerated, especially around the outer radius with large temperature gradient profiles. However, the viscous dissipation rate in the early stage of the chemical reaction is greater because of heat release, which results in weakened turbulent mixing within the mixing regions. We confirm that small-scale structures begin to develop after reshock and then decay over time. During the developing process, helicity also begins to develop, in addition to kinetic energy, viscous dissipation rate, enstrophy, etc. In the present numerical simulations with cylindrical geometry, the fluctuating flow fields evolve from quasi-two-dimensional perturbations, and the generations of helicity can capture this transition process. The weakened fluctuations during shock compression can be explained as the inverse energy cascade, and the chemical reaction can promote this inverse energy cascade process.

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Section: Resultsmentioning

confidence: 99%

Effect of chemical reaction on mixing transition and turbulent statistics of cylindrical Richtmyer–Meshkov instability

Yan

Wang

et al. 2022

J. Fluid Mech.

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“…We shall argue that much of this prior theory and simulation work is either irrelevant to turbulence in real molecular fluids or requires substantial modifications, because effects of thermal noise become significant already at length-scales scales right around the Kolmogorov scale. Laboratory experiments are now beginning to probe these small lengthscales [40,42,43] and may soon provide some evidence of the effects of noise that we predict.…”

Section: Introductionmentioning

confidence: 88%

Dissipation-Range Fluid Turbulence and Thermal Noise

Eyink¹,

Bandak²,

Goldenfeld³

et al. 2021

Preprint

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We revisit the issue of whether thermal fluctuations are relevant for incompressible fluid turbulence, and estimate the scale at which they become important. As anticipated by Betchov in a prescient series of works more than six decades ago, this scale is about equal to the Kolmogorov length, even though that is several orders of magnitude above the mean free path. This result implies that the deterministic version of the incompressible Navier-Stokes equation is inadequate to describe the dissipation range of turbulence in molecular fluids. Within this range, the fluctuating hydrodynamics equation of Landau and Lifschitz is more appropriate. In particular, our analysis implies that both the exponentially decaying energy spectrum and the far-dissipation range intermittency predicted by Kraichnan for deterministic Navier-Stokes will be generally replaced by Gaussian thermal equipartition at scales just below the Kolmogorov length. Stochastic shell model simulations at high Reynolds numbers verify our theoretical predictions and reveal furthermore that inertial-range intermittency can propagate deep into the dissipation range, leading to large fluctuations in the equipartition length scale. We explain the failure of previous scaling arguments for the validity of deterministic Navier-Stokes equations at any Reynolds number and we provide a mathematical interpretation and physical justification of the fluctuating Navier-Stokes equation as an "effective field-theory" valid below some high-wavenumber cutoff Λ, rather than as a continuum stochastic partial differential equation. At Reynolds number around a million, comparable to that in Earth's atmospheric boundary layer, the strongest turbulent excitations observed in our simulation penetrate down to a length-scale of about eight microns, still two orders of magnitude greater than the mean-free-path of air. However, for longer observation times or for higher Reynolds numbers, more extreme turbulent events could lead to a local breakdown of fluctuating hydrodynamics.

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“…This neglect is commonly justified by the idea that there is a strong separation between hydrodynamic scales dominated by turbulent fluctuations and extremely small scales of order the mean-free path length where thermal fluctuations begin to play a role [17]. The smallest turbulent fluid scales below which eddies are damped by viscosity, known as the dissipation range, typically occurs at millimeter scales and there is currently intensive effort, by computation [18][19][20], theory [21][22][23] and experiment [19,24,25], to understand the dynamics and statistics at these scales. The motivation ranges from unraveling the nature of turbulence itself, and the associated unsolved issue of formation of singularities [26], to the phenomena and practical applications mentioned above and others.…”

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confidence: 99%

Thermal noise competes with turbulent fluctuations below millimeter scales

Bandak,

Eyink,

Mailybaev

et al. 2021

Preprint

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Turbulent flows frequently accompany physical, chemical and biological processes, such as mixing, two-phase flow, combustion and even foraging by bacteria and plankton larvae, all of which are in principle subject to thermal fluctuations already on scales of several microns. Nevertheless the large separation between the millimeter scale at which turbulent fluctuations begin to be strongly damped and the mean free path of the fluid has been generally assumed to imply that thermal fluctuations are irrelevant to the turbulent dissipation range. Here we use statistical mechanical estimates to show that thermal fluctuations are not negligible compared to turbulent eddies in the dissipation range. Simulation of the Sabra shell model shows that intermittent bursts of turbulence lead to a fluctuating length scale below which thermal fluctuations are important: over three decades of length, from sub-millimeter scales down to the mean free path, thermal fluctuations coexist with hydrodynamics. Our results imply that thermal fluctuations cannot be neglected when modeling turbulent phenomena in the far dissipation range.

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Three-dimensional analysis of precursors to non-viscous dissipation in an experimental turbulent flow

Abstract: Abstract

Cited by 16 publications

References 35 publications

Effect of chemical reaction on mixing transition and turbulent statistics of cylindrical Richtmyer–Meshkov instability

Effect of chemical reaction on mixing transition and turbulent statistics of cylindrical Richtmyer–Meshkov instability

Dissipation-Range Fluid Turbulence and Thermal Noise

Thermal noise competes with turbulent fluctuations below millimeter scales

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