Geodesic
Topological meaning of the slope of the Kolmogorov spectrum of magnetic turbulence
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 2, pp. 351-366 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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
Mots-clés : $M$-invariant. 
@article{TMF_2021_209_2_a7,
     author = {P. M. Akhmet'ev},
     title = {Topological meaning of the~slope of {the~Kolmogorov} spectrum of magnetic turbulence},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {351--366},
     year = {2021},
     volume = {209},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a7/}
}
TY  - JOUR
AU  - P. M. Akhmet'ev
TI  - Topological meaning of the slope of the Kolmogorov spectrum of magnetic turbulence
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2021
SP  - 351
EP  - 366
VL  - 209
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a7/
LA  - ru
ID  - TMF_2021_209_2_a7
ER  - 
%0 Journal Article
%A P. M. Akhmet'ev
%T Topological meaning of the slope of the Kolmogorov spectrum of magnetic turbulence
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2021
%P 351-366
%V 209
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a7/
%G ru
%F TMF_2021_209_2_a7
P. M. Akhmet'ev. Topological meaning of the slope of the Kolmogorov spectrum of magnetic turbulence. Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 2, pp. 351-366. http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a7/

[1] G. K. Moffat, Vozbuzhdenie magnitnogo polya v provodyaschei srede, Mir, M., 1980

[2] Ya. B. Zeldovich, A. A. Ruzmaikin, D. D. Sokolov, Magnitnye polya v astrofizike, NITs “Regulyarnaya i khaoticheskaya dinamika”, M., Izhevsk, 2006

[3] K.-H. Rädler, “The generation of cosmic magnetic fields”, From the Sun to the Great Attractor (Guanajuato, August 4–11, 1999), Lecture Notes in Physics, 556, eds. D. Page, J. G. Hirsh, Springer, Berlin, 2000, 101–172 | DOI

[4] V. I. Arnold, B. A. Khesin, Topological Methods in Hydrodynamics, Applied Mathematical Sciences, 125, Springer, Cham, 2013 | DOI | MR

[5] U. Frish, Turbulentnost. Nasledie A. N. Kolmogorova, Fazis, M., 1998 | MR | Zbl

[6] P. M. Akhmetev, “K probleme Arnolda o vysshem analoge asimptoticheskogo invarianta Khopfa”, Problemy matematicheskogo analiza, 79 (2015), 25–34 | DOI

[7] V. I. Arnold, The asymptotic Hopf invariant and its applications, preprint, Armenian SSR Academy of Sciences, Erevan, 1974; Selecta Math. Soviet., 5:4 (1986), 327–345 | MR

[8] P. M. Akhmetev, “Potok magnitnoi spiralnosti dlya uravnenii srednego magnitnogo polya”, TMF, 204:1 (2020), 130–141 | DOI | DOI | MR

[9] P. M. Akhmet'ev, I. V. Vyugin, “Dispersion of the Arnold's asymptotic ergodic Hopf invariant and a formula for its calculation”, Arnold Math. J., 6:2 (2020), 199–211 | DOI | MR

[10] P. M. Akhmet'ev, “On asymptotic higher analog of the helicity invariant in magnetohydrodynamics”, J. Math. Sci., 200:1 (2014), 12–25 | DOI | MR

[11] P. M. Akhmet'ev, “On a higher integral invariant for closed magnetic lines”, J. Geom. Phys., 74 (2013), 381–389 | DOI | MR

[12] P. M. Akhmet'ev, “On combinatorial properties of a higher asymptotic ergodic invariant of magnetic lines”, J. Phys.: Conf. Ser., 544 (2014), 012015, 12 pp. | DOI