Turbulent mixing and beyond: non-equilibrium processes from atomistic to astrophysical scales I

Abarzhi, Snezhana I.; Gauthier, Serge; Sreenivasan, Katepalli R.

doi:10.1098/rsta.2012.0436

Cited by 13 publications

(49 citation statements)

References 15 publications

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“…The inertial range is thus expected to be universal because it is independent of both the stirring and dissipative mechanisms. A concrete result is that the so-called longitudinal structure functions, which are moments of velocity component differences, chosen along a prescribed direction, across a separation distance r in the same direction in the inertial range, obey the form CΔu n r D = C n ðerÞ n=3 [3] for all integers n, where C n are constants and the angular brackets imply a suitable average. Only for n = 3 is the result known to be exact (25).…”

Section: Equations and Classical Paradigmsmentioning

confidence: 99%

Turbulent mixing: A perspective

Sreenivasan

2018

Proc. Natl. Acad. Sci. U.S.A.

157

113

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Mixing of initially distinct substances plays an important role in our daily lives as well as in ecological and technological worlds. From the continuum point of view, which we adopt here, mixing is complete when the substances come together across smallest flow scales determined in part by molecular mechanisms, but important stages of the process occur via the advection of substances by an underlying flow. We know how smooth flows enable mixing but less well the manner in which a turbulent flow influences it; but the latter is the more common occurrence on Earth and in the universe. We focus here on turbulent mixing, with more attention paid to the postmixing state than to the transient process of initiation. In particular, we examine turbulent mixing when the substance is a scalar (i.e., characterized only by the scalar property of its concentration), and the mixing process does not influence the flow itself (i.e., the scalar is “passive”). This is the simplest paradigm of turbulent mixing. Within this paradigm, we discuss how a turbulently mixed state depends on the flow Reynolds number and the Schmidt number of the scalar (the ratio of fluid viscosity to the scalar diffusivity), point out some fundamental aspects of turbulent mixing that render it difficult to be addressed quantitatively, and summarize a set of ideas that help us appreciate its physics in diverse circumstances. We consider the so-called universal and anomalous features and summarize a few model studies that help us understand them both.

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Section: Equations and Classical Paradigmsmentioning

confidence: 99%

Turbulent mixing: A perspective

Sreenivasan

2018

Proc. Natl. Acad. Sci. U.S.A.

157

113

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“…Particularly in RT mixing induced by constant acceleration, the length scale in the acceleration direction grows quadratically with time [1][2][3][4][5][6]. RTI and associated mixing play important role in a broad range of processes in nature and technology [7][8][9]. Examples include supernovae, inertial confinement fusion, material transformation under impact, and fossil fuel extraction [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…RTI and associated mixing play important role in a broad range of processes in nature and technology [7][8][9]. Examples include supernovae, inertial confinement fusion, material transformation under impact, and fossil fuel extraction [7][8][9][10]. The development of reliable methods of analysis of experimental and numerical data is required to better understand RT-relevant phenomena and to achieve a bias-free interpretation of the results [7,11,12].…”

Section: Introductionmentioning

confidence: 99%

“…There are several challenges in studying RTI and RT mixing: the stringent requirements on the flow implementation, diagnostics and control in experiments [7,[11][12][13][14][15][16]; the necessity to accurately capture interfaces and small-scale dissipation processes in simulations [17][18][19][20]; and the need to account for the non-local, multi-scale, anisotropic, heterogeneous and statistically unsteady character of the dynamics in theory [3,11,21,22]. Furthermore, a systematic interpretation of RT dynamics from data alone is not straightforward and requires a substantial range of highly resolved temporal and spatial scales [11,13].…”

Section: Introductionmentioning

confidence: 99%

“…In this work, the properties of RT mixing are studied through scrupulous data analysis of experimental data, guided by group theory considerations [7,11]. Group theory outlines the invariance-based properties of fluctuations, including their spectra and the span of arXiv:1908.03977v1 [physics.flu-dyn] 12 Aug 2019 scales [7,11,23].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Whittle maximum likelihood estimate of spectral properties of Rayleigh-Taylor interfacial mixing using hot-wire anemometry experimental data

Pfefferlé

Abarzhi

2020

Phys. Rev. E

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The Rayleigh-Taylor instability (RTI) occurs in a broad range of processes in nature and technology. Analysing the power density spectrum of fluctuations in Rayleigh-Taylor (RT) flow is a means of highlighting characteristic length-and time-scales, anisotropies and anomalous processes. Raw time series from hot-wire anemometry measurements of Rayleigh-Taylor interfacial mixing experiment by Akula et al., JFM 816, 619-660 (2017) are considered as a sample case to adjust the parameters of a model power density spectrum. The results suggest that the power density spectrum of one of the flow components can be confidently modelled as the product of a power law and an exponential. The data analysis is based on Whittle's approximation of the power density spectrum for independent zero-mean near-Gaussian signals to construct a Maximum likelihood Estimator (MLE) of the parameters. Those that maximise the log-likelihood are computed numerically through Newton-Raphson iteration. The Hessian of the log-likelihood is used to evaluate the Fisher information matrix and provide an estimate of the statistical error on the obtained parameters. The Kolmogorov-Smirnov test is used to verify the hypothesis that the ratio between the observed periodogram and the estimated power density spectrum follows a chi-squared probability distribution. This step is performed to show goodness-of-fit. We also study the dependence of the model parameters on the range of mode numbers over which the fit is performed.

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Effect of initial perturbation amplitude on Richtmyer-Meshkov flows induced by strong shocks

Dell

Stellingwerf²,

Abarzhi

2015

Physics of Plasmas

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We systematically study the effect of the initial perturbation on Richtmyer-Meshkov (RM) flows induced by strong shocks in fluids with contrasting densities. Smooth Particle Hydrodynamics simulations are employed. A broad range of shock strengths and density ratios is considered. The amplitude of the initial single mode sinusoidal perturbation of the interface varies from 0% to 100% of its wavelength. The simulations results are compared, wherever possible, with four rigorous theories, and with other experiments and simulations, achieving good quantitative and qualitative agreement. Our study is focused on early time dynamics of the Richtmyer-Meshkov instability (RMI). We analyze the initial growth-rate of RMI immediately after the shock passage, when the perturbation amplitude increases linearly with time. For the first time, to the authors' knowledge, we find that the initial growth-rate of RMI is a non-monotone function of the initial perturbation amplitude, thus restraining the amount of energy that can be deposited by the shock at the interface. The maximum value of the initial growth-rate depends on the shock strength and the density ratio, whereas the corresponding value of the initial perturbation amplitude depends only slightly on the shock strength and density ratio.

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Turbulent mixing and beyond: non-equilibrium processes from atomistic to astrophysical scales I

Cited by 13 publications

References 15 publications

Turbulent mixing: A perspective

Turbulent mixing: A perspective

Whittle maximum likelihood estimate of spectral properties of Rayleigh-Taylor interfacial mixing using hot-wire anemometry experimental data

Effect of initial perturbation amplitude on Richtmyer-Meshkov flows induced by strong shocks

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