Magnetic Field Dynamical Regimes in a Large-Scale Low-Mode α Ω-Dynamo Model with Hereditary α -Quenching by Field Energy

Olga Sheremetyeva ()
Additional contact information
Olga Sheremetyeva: Laboratory of Physical Process Modeling, Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences, Mirnaya Str., 7, Paratunka, 684034 Kamchatka, Russia

Mathematics, 2023, vol. 11, issue 10, 1-14

Abstract: The article considers a large-scale model of an α Ω -dynamo in the low-mode approximation. The intensity of the α -effect is regulated by a process that depends on the energy of the magnetic field and has hereditarity properties (finite “memory”). The regulation process is included in the MHD-system in the form of an additive correction. The action character of the process is defined by the alternating kernel with variable parameters: the damping frequency and the damping coefficient. The Reynolds number and the α -effect measure are the control parameters of the system. Information about the action of a large-scale generator is contained in the Reynolds number, and that about the action of a turbulent one is contained in the measure of the α -effect. The stability of the solution of the MHD-system is studied depending on the values of the control parameters and the parameters of the alternating kernel. Based on the results of numerical simulation of the dynamical regimes, limitations are determined for the values of the model parameters at which the regimes are reproduced against the background of small oscillations of the viscous liquid velocity field. The results of the study of the stability of solutions and numerical simulations of the dynamical regimes are represented on the phase plane of the control parameters. The paper investigates the question of changing the pattern on the phase plane depending on the values of the damping coefficient, the damping frequency, and the waiting time. A comparison is made with the results obtained earlier, when the α -effect intensity is a constant or is regulated by a process with an exponential kernel and the same values of the damping coefficient.

Keywords: ??-dynamo; low-mode dynamo model; ?-quenching; magnetic field regimes; reversals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/10/2297/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/10/2297/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:10:p:2297-:d:1147279

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().