No feedback is possible in a small-scale turbulent magnetic field

Zybin, K. P.; Il'yn, A. S.; Kopyev, A. V.; Sirota, V. A.

doi:10.1209/0295-5075/132/24001

Cited by 4 publications

(1 citation statement)

References 23 publications

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“…Namely, the theoretical analysis and numerical simulation confirm that, as µ → ∞, the increment γ(µ, F ) converges to the value γ(F ) found for the Batchelor regime. This is also not trivial: for instance, this equality does not hold for two-dimensional flows (Kolokolov 2017;Schekochihin et al 2002a) or for higher-order correlators in three-dimensional flows (Zybin et al 2020). The Kazantsev equation corresponds to the infinitetime limit; the convergence of the solutions in the limit P r m → ∞ (and its coincidence with the value obtained for the Batchelor case) means that the limits P r m → ∞ and t → ∞ commutate.…”

Section: Discussionmentioning

confidence: 99%

Non-Gaussian generalization of the Kazantsev-Kraichnan model

Kopyev,

Kiselev,

Il'yn

et al. 2021

Preprint

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We consider a natural generalization of the Kazantsev-Kraichnan model for small-scale turbulent dynamo. This generalization takes account of statistical time asymmetry of a turbulent flow, and, thus, allows to describe velocity fields with energy cascade. For three-dimensional velocity field, generalized Kazantsev equation is derived, and evolution of the second order magnetic field correlator is investigated for large but finite magnetic Prandtl numbers. It is shown that as P r 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 depends essentially on the Prandtl number.

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Section: Discussionmentioning

confidence: 99%

Non-Gaussian generalization of the Kazantsev-Kraichnan model

Kopyev,

Kiselev,

Il'yn

et al. 2021

Preprint

Self Cite

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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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