Sub-Kolmogorov droplet dynamics in isotropic turbulence using a multiscale lattice Boltzmann scheme

Milan, Felix; Biferale, Luca; Sbragaglia, Mauro; Toschi, Federico

doi:10.1016/j.jocs.2020.101178

Cited by 9 publications

(6 citation statements)

References 59 publications

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“…which is the physical-space analogue of the scalar spectrum (2) found by Kraichnan [25]. The correction due to thermal noise in the viscous-diffusive range can be evaluated by a joint expansion of the exact solution (69) in r/ B and = σ/ B and, using r 1 / B = 3 2 + O( 2 ), one recovers the result (64). As we show in the next subsection, the concentration spectrum E c (k) corresponding to (69) by Fourier transform can be found exactly and this result yields the two limiting power laws, ( 63) and (65), thus verifying the giant concentration fluctuations in the viscous-diffusive range but further describing in detail the transition between the two power-law regimes.…”

supporting

confidence: 60%

“…The main message of our work for turbulence theory is that thermal noise completely alters the character of the viscous-diffusive range of high Schmidt-number turbulent advection, leading to fundamentally different predictions than those based on deterministic Navier-Stokes dynamics. This is likely to be true also for other physical processes in turbulent flows that involve essentially the sub-Kolmogorov scale motions, such as combustion [59][60][61], condensation [62][63][64] and locomotion of microorganisms [65][66][67], not to speak of the intrinsic nonlinear turbulent dynamics itself. The presence of giant concentration fluctuations in turbulent flows should not have been unexpected, because they are a generic feature of diffusive mixing far from global equilibrium.…”

Section: Introductionmentioning

confidence: 99%

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High Schmidt-Number Turbulent Advection and Giant Concentration Fluctuations

Eyink¹,

Jafari²

2021

Preprint

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We consider the effects of thermal noise on the Batchelor-Kraichnan theory of high Schmidtnumber mixing in the viscous dissipation range of turbulent flows at sub-Kolmogorov scales. Starting with the nonlinear Landau-Lifschitz fluctuating hydrodynamic equations for a binary fluid mixture at low Mach numbers, we justify linearization around the deterministic Navier-Stokes solution in the dissipation range. For the latter solution we adopt the standard Kraichnan model, a Gaussian random velocity with spatially-constant strain but white-noise in time. Then, following prior work of Donev, Fai & vanden-Eijnden, we derive asymptotic high-Schmidt limiting equations for the concentration field, in which the thermal velocity fluctations are exactly represented by a Gaussian random velocity that is likewise white in time. We obtain the exact solution for concentration spectrum in this high-Schmidt limiting model, showing that the Batchelor prediction in the viscousconvective range is unaltered. Thermal noise dramatically renormalizes the bare diffusivity in this range, but the effect is the same as in laminar flow and thus hidden phenomenologically. However, in the viscous-diffusive range at scales below the Batchelor length (typically micron scales) the predictions based on deterministic Navier-Stokes equations are drastically altered by thermal noise. Whereas the classical theories predict rapidly decaying spectra in the viscous-diffusive range, either Gaussian or exponential, we obtain a k −2 power-law spectrum over a couple of decades starting just below the Batchelor length. This spectrum corresponds to non-equilibrium giant concentration fluctuations (GCF's), which are due to the imposed concentration variations being advected by thermal velocity fluctuations and which are experimentally well-observed in quiescent fluids. At higher wavenumbers, the concentration spectrum instead goes to a k 2 equipartition spectrum due to equilibrium molecular fluctuations. We work out detailed predictions for water-glycerol and water-fluorescein mixtures. Finally, we discuss broad implications for turbulent flows and novel applications of our methods to experimentally accessible laminar flows.

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confidence: 60%

Section: Introductionmentioning

confidence: 99%

High Schmidt-Number Turbulent Advection and Giant Concentration Fluctuations

Eyink¹,

Jafari²

2021

Preprint

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“…Current theory and numerical modelling of all these processes in turbulent flows omit thermal noise completely, e.g. in the case of high Schmidt/Prandtl-number scalar mixing [133][134][135], dynamics of droplets and bubbles [136][137][138], chemical combustion [139][140][141], and locomotion in turbulent flows [142,143]. The possibility exists in all of these cases of interesting interplay between turbulence and thermal effects, which might yield clear experimental signatures.…”

Section: Structure Functionsmentioning

confidence: 99%

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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“…These include high Schmidt/Prandtlnumber scalar mixing [1], droplet and bubble formation [2,3], locomotion of micro-organisms [4], combustion [5,6], and others. Often the relevant flows are turbulent, in which case all current approaches to model these processes -high Schmidt-number scalar mixing [7,8], droplet and bubble formation [9,10], cellular motility [11,12], and combustion [13][14][15][16] -focus on turbulent fluctuations due to fluid inertia damped by viscosity and ignore thermal effects completely. 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].…”

mentioning

confidence: 99%

“…Plotted as well in Fig. 4 is the PDF of N vis (u), defined as in (10). This PDF is plotted together with a standard multifractal model of the type developed for deterministic Navier-Stokes [57], here constructed using the ansatz [58] N vis (h) = Round log 2 (Re)…”

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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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Sub-Kolmogorov droplet dynamics in isotropic turbulence using a multiscale lattice Boltzmann scheme

Cited by 9 publications

References 59 publications

High Schmidt-Number Turbulent Advection and Giant Concentration Fluctuations

High Schmidt-Number Turbulent Advection and Giant Concentration Fluctuations

Dissipation-Range Fluid Turbulence and Thermal Noise

Thermal noise competes with turbulent fluctuations below millimeter scales

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