Exact result for mixed triple two-point correlations of velocity and velocity gradients in isotropic turbulence

Kopyev, A. V.; Zybin, K. P.

doi:10.1080/14685248.2018.1511055

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…На основании колмогоровского закона «4/5» (Колмогоров, 1941; Ландау, Лифшиц, 2006) получены аналитические соотношения для тройных двухточечных корреляций градиентов скорости и скорости в однородной изотропной несжимаемой турбулентности (Kopyev, Zybin, 2018). Соответствующий тензор корреляции может быть выражен через скорость диссипации, корреляционную функцию второго порядка для продольного приращения скорости и новую скалярную функцию.…”

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“…Жуковского» за счет гранта Российского научного фонда (проект №17-11-01271). Sciences, Moscow, 119991, Russia, e-mail: kopyev@lpi.ru 2 National Research University Higher School of Economics, Moscow, 101000, Russia Submitted 25.12.2018, accepted 30.01.2019 On the basis of Kolmogorov's 4/5 law (Kolmogorov, 1941;Landau, Lifschitz 1975) analytical relations for triple two-point correlations of velocity and velocity gradients in homogeneous isotropic incompressible turbulence are derived (Kopyev, Zybin, 2018). The corresponding correlation tensor can be expressed in terms of the dissipation rate, the second-order correlation function for the longitudinal velocity increment, and the new scalar function of distance between the points.…”

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Mixed Triple Two-Point Correlations of Velocity and Velocity Gradients in Homogeneous Isotropic Turbulence

Kopyev

Zybin

2019

JOR

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On the basis of Kolmogorov’s 4/5 law (Kolmogorov, 1941; Landau, Lifschitz 1975) analytical relations for triple two-point correlations of velocity and velocity gradients in homogeneous isotropic incompressible turbulence are derived (Kopyev, Zybin, 2018). The corresponding correlation tensor can be expressed in terms of the dissipation rate, the second-order correlation function for the longitudinal velocity increment, and the new scalar function of distance between the points. However, some components of the tensor do not depend on the new function. The derived analytical results are in agreement with the data obtained from direct numerical simulations. The function can be well approximated in the inertial range by a constant value that depends on the dissipation only. The application of the obtained correlators in the turbulent transport theory is discussed (Il’yn, Sirota, Zybin, 2016; Kazantsev, 1968). The study was performed in Central Aerohydrodynamic Institute (TsAGI) with the funding of Russian Science Foundation (project No. 17-11-01271).

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Mixed Triple Two-Point Correlations of Velocity and Velocity Gradients in Homogeneous Isotropic Turbulence

Kopyev

Zybin

2019

JOR

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Suppression of small-scale dynamo in time-irreversible turbulence

Kopyev,

Il’yn,

Sirota

et al. 2023

Monthly Notices of the Royal Astronomical Society

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The conventional theory of small-scale magnetic field generation in a turbulent flow considers time-reversible random flows. However, real turbulent flows are known to be time irreversible: the presence of energy cascade is an intrinsic property of turbulence. We generalize the ’standard’ model to account for the irreversibility. We show that even small time asymmetry leads to significant suppression of the dynamo effect at low magnetic Prandtl numbers, increases the generation threshold and may even make generation impossible for any magnetic Reynolds number. We calculate the magnetic energy growth rate as a function of the parameters of the flow.

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Non-Gaussian Generalization of the Kazantsev–Kraichnan Model for a Turbulent Dynamo

Kopyev

Kiselev

Il'yn

et al. 2022

ApJ

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We consider a natural generalization of the Kazantsev–Kraichnan model for a small-scale turbulent dynamo. This generalization takes into account the statistical time asymmetry of a turbulent flow and thus allows one to describe velocity fields with energy cascade. For three-dimensional velocity fields, a generalized Kazantsev equation is derived, and the evolution of the second-order magnetic field correlator is investigated for large but finite magnetic Prandtl numbers. It is shown that as Pr m → ∞, the growth increment tends to the limit known from the T-exponential (Lagrangian deformation) method. Magnetic field generation is shown to be weaker than that in the Gaussian velocity field for any direction of the energy cascade and essentially depends on the Prandtl number.

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Exact result for mixed triple two-point correlations of velocity and velocity gradients in isotropic turbulence

Cited by 3 publications

References 28 publications

Mixed Triple Two-Point Correlations of Velocity and Velocity Gradients in Homogeneous Isotropic Turbulence

Mixed Triple Two-Point Correlations of Velocity and Velocity Gradients in Homogeneous Isotropic Turbulence

Suppression of small-scale dynamo in time-irreversible turbulence

Non-Gaussian Generalization of the Kazantsev–Kraichnan Model for a Turbulent Dynamo

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