Our website uses cookies. By continuing to use this site, you agree to our use of cookies in accordance with this notice and the Terms of Use.
Rules for authors Editorial board
Policies
Copyright Policy Open access policy Publishing Ethics Peer review process
Archive ISSN 1681-1208 (Online)
Submit manuscript
Russian Journal of Earth Sciences
Journals / Russian Journal of Earth Sciences / Volume 23 Issue 5 / Linear perturbations of the Bloch type of space-periodic magnetohydrodynamic steady states. III. Asymptotics of branching
UDC 550.8.013 CSCSTI 37.01 BISAC SCI UDC 537.84 CSCSTI 37.15 CSCSTI 37.25 CSCSTI 37.31 CSCSTI 38.01

LINEAR PERTURBATIONS OF THE BLOCH TYPE OF SPACE-PERIODIC MAGNETOHYDRODYNAMIC STEADY STATES. III. ASYMPTOTICS OF BRANCHING Linear perturbations of the Bloch type of space-periodic magnetohydrodynamic steady states. III. Asymptotics of branching

Published in Russian Journal of Earth Sciences · Volume 23, Issue 5 · Pages 1–16 · Rubric: ORIGINAL ARTICLES
DOI: https://doi.org/10.2205/2023ES000841
Received: 22.11.2022 Accepted: 07.03.2023 Published: 15.12.2023 Language of publication: RUS
Authors
R
R Chertovskih
ORCID Scopus ResearcherID
V
V Zheligovsky
ABSTRACT
The previous paper of this series presented the results of a numerical investigation of the dependence of the dominant growth rates of Bloch eigenmodes on the diffusivity parameters (the molecular viscosity ν and molecular magnetic diffusivity η) in three linear stability problems: the kinematic dynamo problem, and the hydrodynamic and MHD stability problems for steady spaceperiodic flows and MHD states. The dominant eigenmodes (i.e., the stability modes, whose growth rates are maximum over the wave vector q of the planar wave involved in the Bloch modes) comprise branches. In some branches, the dominant growth rates are attained for constant half-integer q. In all the three stability problems for parity-invariant steady states, offshoot branches, stemming from the branches of this type, were found, in which the dominant growth rates are attained for q depending on ν and/or η. We consider now such a branching of the dominant magnetic modes in the kinematic dynamo problem, where an offshoot stems from a branch of neutral eigenmodes for q = 0, and construct power series expansions for the offshoots and the associated eigenvalues of the magnetic induction operator near the point of bifurcation. We show that the branching occurs for the molecular magnetic diffusivities, for which the two eigenvalues of the eddy diffusivity operator become imaginary, and magnetic field generation by the mechanism of the negative eddy diffusivity ceases. The details of branching in the other linear stability problems under consideration are distinct.
KEYWORDS
Power series expansion, asymptotics, kinematic dynamo problem, Bloch magnetic mode, branching, neutral eigenmodes, magnetic eddy diffusivity, scale separation.
Funding
The project was financed by the grant No. 22-17-00114 of the Russian Science Foundation, https://rscf.ru/project/22-17-00114/.
Text References
Text
Text (PDF)
Read Download

1. Andrievsky, A., A. Brandenburg, A. Noullez, and V. Zheligovsky (2015), Negative magnetic eddy diffusivities from the test-field method and multiscale stability theory, The Astrophysical Journal, 811(2), 135, https://doi.org/10.1088/0004-637x/811/2/135.

2. Arnol’d, V., Y. Zel’dovich, A. Ruzmaikin, and D. Sokolov (1982), Steady-state magnetic field in a periodic flow, Soviet Physics-Doklady, 266(6), 1357-1361 (in Russian).

3. Chertovskih, R., and V. Zheligovsky (2023a), Linear perturbations of the Bloch type of space-periodic magnetohydrodynamic steady states. I. Mathematical preliminaries, Russian Journal of Earth Sciences, 23, ES3001, https://doi.org/10.2205/2023ES000834.

4. Chertovskih, R., and V. Zheligovsky (2023b), Linear perturbations of the Bloch type of space-periodic magnetohydrodynamic steady states. II. Numerical results, Russian Journal of Earth Sciences, 23, ES4004, https://doi.org/10.2205/2023ES000838.

5. Rasskazov, A., R. Chertovskih, and V. Zheligovsky (2018), Magnetic field generation by pointwise zero-helicity threedimensional steady flow of an incompressible electrically conducting fluid, Physical Review E, 97(4), 043,201, https://doi.org/10.1103/PhysRevE.97.043201.

6. Zheligovsky, V. (2011), Large-Scale Perturbations of Magnetohydrodynamic Regimes, 330 pp., Springer Berlin Heidelberg, https://doi.org/10.1007/978-3-642-18170-2.

This work is licensed under Creative Commons Attribution 4.0 International
PDF Text JATS XML
The contact persons
Alexei Gvishiani
Chief Editor
Alexei Gvishiani
rjes@wdcb.ru
Boris Dzeboev
Deputy Chief Editor
Boris Dzeboev
rjes@wdcb.ru
Ernest Kedrov
Managing Editor
Ernest Kedrov
ernest.kedrov@ya.ru
Natalya Kareva
Responsible Secretary
Natalya Kareva
rjes@wdcb.ru
3403
downloads
Scopus Web of Science Crossref RINC Science Index Geodesy and cartography GeoRef Cyberleninka Directory of Open Access Journals RCSI
CC
This work is licensed under Creative Commons Attribution 4.0 International Creative Commons
ISSN 1681-1208 (Online)
© gcras.editorum.ru
Agreement Personal data protection and processing policy Support Powered by Editorum, 2026 Instructions
Login or Create
* Forgot your password?