Vestnik КRAUNC. Fiz.-Mat. Nauki. 2025. vol. 52. no. 3. P. 95 – 110. ISSN 2079-6641

MATHEMATICAL MODELING
https://doi.org/10.26117/2079-6641-2025-52-3-95-110
Research Article
Full text in Russian
MSC 68P05, 86A25, 65M60

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Basic Modes Parameters and Geodynamo Spectral Models Coefficients Database

G. M. Vodinchar^{\ast}¹, E. A. Kazakov¹, S. S. Lisyutkin¹²

¹Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Mirnaya str., 7, Paratunka, Kamchatka, Russia, 684034
²Vitus Bering Kamchatka State University, Pogranichnaya str., 4, Petropavlovsk-Kamchatsky, Russia, 683032

Abstract. The geodynamo spectral models are constructed based on a finite set of basic stationary fields (modes). The velocity, temperature, and magnetic induction fields are represented in this models as linear combinations of the basic modes with time-dependent coefficients (amplitudes). A dynamic system is constructed for the amplitudes, whose coefficients (Galerkin coefficients) are calculated based on the modes. Therefore, modes and coefficients are necessary to construct the model. The most natural set of basic modes are the eigenmodes of free decay of velocity, temperature, and magnetic induction in the Earth’s core. Each such mode is defined by a standard mathematical expression, but this expression contains several numerical parameters. One of these parameters is the eigenvalue. It is convenient to store the mode parameters and the Galerkin coefficients calculated from them in a structured form in a relational database (DB). This paper describes the structure of a DB developed for these purposes. Based on an analysis of the structure of the eigenmodes and the identification of attributes characterizing the modes, the structures of the relational tables of the DB and the relationships between them are determined. The structure of Galerkin’s coefficients is analyzed for their representation in a database. Based on this analysis, a structure for relational tables for the coefficients and the relationships between them and the mode tables is developed. The developed DB is integrated into a computational system for geodynamo modeling. In this system, the DB serves as a data source for numerical modeling modules. Furthermore, the modules included in the system for calculating eigenmode parameters and Galerkin coefficients allow new records to be added to the DB. The interaction between the computational modules and the database is also described in the article.

Key words: geodynamo, spectral models, free decay modes, Galerkin’s method, relational databases.

Received: 13.11.2025; Revised: 18.11.2025; Accepted: 20.11.2025; First online: 21.11.2025

For citation. Vodinchar G. M., Kazakov E. A., Lisyutkin S.,S. Basic Modes Parameters and Geodynamo
Spectral Models Coefficients Database. Vestnik KRAUNC. Fiz.-mat. nauki. 2025, 52: 3, 95-110. EDN: HQPQOS. https://doi.org/10.26117/2079-6641-2025-52-3-95-110.

Funding. The study was carried out under the State Subject of IKIR FEB RAS (reg. № 124012300245-2).

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

^{\ast}Correspondence: E-mail: gvodinchar@ikir.ru

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Vodinchar G. M., Kazakov E. A., Lisyutkin S.,S., 2025

© Institute of Cosmophysical Research and Radio Wave Propagation, 2025 (original layout, design, compilation)

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Vodinchar Gleb Mikhailovich – PhD (Phys & Math), Docent, Leading Researcher, Institute of Cosmophysical Researh and Radio Wave Propagation, Paratunka, Kamchatka, Russia, ORCID 0000-0002-5516-1931.

Kazakov Evgeny Anatolyevich – Junior Research, Institute of Cosmophysical Researh and Radio Wave Propagation, Paratunka, Kamchatka, Russia, ORCID 0000-0001-7235-4148.

Lisyutkin Semyon Sergeevich – Programmer, Institute of Cosmophysical Researh and Radio Wave Propagation, Paratunka, Kamchatka, Russia; MS student, Vitus Bering Kamchatka State University, Petropavlovsk-Kamchatsky, Russia, ORCID 0009-0000-9076-1521.

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