Solar activity leaves traces in terrestrial archives: in the rings of a Yakushima cedar that lived for 1924 years, 11- and 22-year periodicities were found even during grand minima such as the Maunder minimum. Neighboring works in the archive explore solar wind, tidal rhythms, neutrino oscillations, and gravitational waves from neutron stars, but this article stands apart: it constructs a phenomenological model linking the solar dynamo cycle to oceanic oscillations. There are no direct analogs among the nearest neighbors; the closest thematically is a study of neutrino oscillations, but that concerns particle physics, not macroscopic rhythms.
The author analyzes the 315-year sunspot number series (1700–2015) using Fourier transform and selects two peaks at the 2σ significance level: 12.05 years and 9.52 years. These two periods become the frequencies of two harmonic oscillators. Their superposition gives beats: an average period of 10.6 years and modulation with a period of 89 years. The same procedure is applied to El Niño data: observed periods of 5.35±0.6 years and 3.55±0.25 years are taken; their combined signal produces an envelope with a period of 21.5±5 years. To connect with solar physics, helioseismic observations from SDO/MDI are used, revealing a two-layer meridional circulation: the outer cell flows from the equator to the poles at depths of 0.82–0.91 solar radii, and the inner cell at 0.70–0.82 radii. The toroidal currents of these cells are considered as coupled circuits interacting according to Lenz's law.
The superposition of two solar oscillators with periods of 12.05 and 9.52 years reproduces the 89-year Gleissberg cycle, known from independent carbon-13 data in cedar rings. However, the model does not reproduce the 22-year periodicity in solar data. But applying the same model to El Niño with periods of 5.35 and 3.55 years yields a 21.5±5-year envelope that matches the 22-year signal in tree rings. The author estimates the strength of the toroidal current in the outer cell at 3×$10^{11}$ A, based on a field of $10^{-4}$ T at the pole, and in the convergence zone of the cells at a depth of 0.85 solar radii expects fields up to 1000 gauss, comparable to sunspot fields. Two types of cosmic-ray minimum shapes (flat and sharp peaks) are explained by which oscillator, outer or inner, dominates at a given time.
The work proposes a unified mechanism for the solar dynamo and oceanic oscillations, reducing complex dynamics to the interaction of two modes. Unlike neighboring studies that either analyze individual signals (solar wind, tides, neutrinos) or build numerical models, here a simple analytical scheme is given that links the helioseismic structure of the convective zone to observed periods. This is a phenomenological bridge between microscopic turbulence and macroscopic cycles, similar to the connection between thermodynamics and statistical mechanics.
The model can be extended by including nonlinear interactions between cells, asymmetry between the northern and southern hemispheres, and stochastic forcing by turbulence. It is promising to link oscillator parameters to the observed meridional flow speed (about 10 m/s at high latitudes) and to test predictions against long records of sunspots and cosmic rays. For El Niño, it is worth investigating how coupled oscillators interact with the Pacific Decadal Oscillation and other modes.
The results are important for solar physics, climatology, and dendrochronology: they offer an interpretation of the 22-year signal in tree rings as a response to El Niño rather than directly to solar activity.
Test the model against independent data: long sunspot records, isotope-based reconstructions of solar activity, and real-time observations of meridional circulation. Compare predictions with global climate models that include El Niño.
In solar physics, the origin of the 22-year magnetic cycle and its connection to meridional circulation remains unresolved. The coupled-oscillator model offers a specific mechanism but does not explain why the cell periods are exactly as they are or how they synchronize. For climatology, the question remains open as to how oceanic oscillations modulate regional climate on decadal timescales.
The Yakushima cedar, whose rings revealed the 22-year signal, lives on Yakushima Island, where annual precipitation reaches 4000–10000 mm, making it one of the wettest places in Japan.