This article is cited in 1 paper

Topological meaning of the slope of the Kolmogorov spectrum of magnetic turbulence

P. M. Akhmet'ev

Pushkov Institute of Terrestrial Magnetism, the Ionosphere, and Radio Wave Propagation, Troitsk, Moscow, Russia

Abstract: It is well known that the magnetic helicity is not a single invariant in ideal magnetohydrodynamics. We study the problem of whether the exponent $-1.7$ of the slope of the turbulent spectrum of magnetic energy can be explained. An affirmative answer is obtained under the assumption that the quasiperiodic magnetic field is freely distributed over the scale. The answer is based on the use of the asymptotic Hopf invariant and the $M$-invariant (numerical measure of knottedness of magnetic lines).

Keywords: magnetic helicity, magnetic energy, $M$-invariant.

Received: 20.05.2021
Revised: 02.06.2021

DOI: 10.4213/tmf10130

 English version: Theoretical and Mathematical Physics, 2021, 209:2, 1620–1632

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