Grounding Rikitake-like conceptual dynamos in mean-field MHD: the derivation and geophysical scaling of the most basic reversal dynamo model

Clicks: 33
ID: 330452
2026
Free PDF
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This article has not been analysed, so there is no overall score — reader engagement is measured and shown alongside.
AI Quality Assessment
Not analyzed
Readership in this journal
Emerging

Ranked #18 of 338 articles by views in geophysical journal international

Most read Least read

Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 338 in total.

Mint this article as an NFT
Not yet minted

Create a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.

5 SUSD one-off · no wallet required
Sign in to mint
Abstract
Summary We report the first explicit derivation of the Rikitake dynamo as a direct approximation of mean-field magnetohydrodynamics (MHD), establishing a systematic connection between a classical conceptual reversal model and the governing large-scale field equations. Starting from the mean-field induction and momentum equations, we show that a strongly truncated Galerkin expansion already retains the nonlinear couplings among magnetic induction, diffusion, convective driving, and Lorentz-force feedback required for reversal dynamics. Within this framework, a family of low-dimensional models arise as a limiting approximation of the reduced mean-field system. Placing further constraints on the Galerkin basis functions results in what we call the canonical Rikitake model. We provide an explicit harmonic realization that fulfills these constraints and preserves the minimal nonlinear structure capable of producing irregular oscillations and spontaneous polarity reversals. The reduced parameters acquire clear physical meaning in terms of inductive regeneration, effective magnetic diffusivity, forcing, and magnetic backreaction. Using representative outer-core scalings, we obtain characteristic amplitudes and timescales consistent with geophysical estimates, including observed chron durations. Numerical integrations reproduce several features of geomagnetic variability, including polarity reversals, irregular oscillations, and extended intervals of persistent polarity. The canonical model supports both short and long chrons, including superchrons, whereas the harmonic realization yields only short chrons, indicating that richer basis functions may be needed to recover broader reversal statistics. These results place Rikitake-type models on firm physical grounds and provide a route toward systematically constructed low-dimensional dynamos derived from MHD.
Reference Key
openalex_W7214755974 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Dániel Jánosi, Mátyás Herein
Are you one of these authors? Claim your profile
Journal geophysical journal international
Year 2026
DOI
10.1093/gji/ggag390
URL
https://doi.org/10.1093/gji/ggag390
Keywords Keywords not found

Citations

No citations found. To add a citation, contact the admin at info@scimatic.org

Comments

No comments yet. Be the first to comment on this article.