The Sun as Two Pendulums: Why the Star's Rhythm Speeds Up and Then Pauses ✎

Original: "Application of Coupled Harmonic Oscillator model to Solar Activity and El Niño Phenomena"
· Yasushi Muraki
arXiv:1706.09105 · 2017-06-28 · arXiv non-exclusive · independent analysis · 1 min
Two plasma flows inside the Sun swing like pendulums, and their combined rhythm explains the 89-year cycle and the 22-year signal in tree rings.

Two pendulums swinging side by side gradually begin to influence each other. The same happens with two plasma flows inside the Sun. One flows closer to the surface, the other deeper, and each has its own rhythm: 12.05 and 9.52 years. When the two oscillations combine, a slow beat emerges: the strength of the combined rhythm rises and falls every 89 years. This explains the Gleissberg cycle, the long wave in solar activity.

The two flows inside the Sun exchange energy like two pendulums on a common support. The outer flow moves from the equator to the poles, the inner one deeper, and their interaction sets the overall rhythm. The current in the outer flow is 3×$10^{11}$ amperes, and where the flows meet, the magnetic field reaches 1000 gauss, as strong as in sunspots.

The same approach explains the ocean as well. El Niño has two oscillations: 5.35 and 3.55 years. Their sum produces a slow beat with a period of 21.5 years. That is exactly the signal found in the rings of the Yakushima cedar, which has been growing on Yakushima Island since 1924. So the 22-year rhythm in the wood was left not by the Sun but by the warm current of the Pacific Ocean. This used to be a puzzle, but now it all fits: two pendulums in the sky and two in the sea leave a common mark on the Earth.

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.

\psi = \sin(\omega_A t + \alpha) + \sin(\omega_B t) = 2 \sin\left(\frac{\omega_A+\omega_B}{2}t + \frac{\alpha}{2}\right) \cos\left(\frac{\omega_A-\omega_B}{2}t + \frac{\alpha}{2}\right)
The sum of two sinusoids with close frequencies gives an oscillation at the average frequency and a slow envelope at the difference frequency.
B = \frac{\mu I}{2\sqrt{8} R}
The magnetic field at the pole is produced by a toroidal current I flowing at distance R; hence the current is estimated at 3×10^11 A.
Concepts
recharge oscillator model El Niño-Southern Oscillation ENSO Multivariate ENSO Index Jin-Timmermann model La Niña ocean-atmosphere coupling El Niño index solar cycle mixed mode oscillations quasi biennial oscillation seasonal cycle seasonal forcing Indian Ocean capacitor effect TAO/TRITON moorings interannual variability natural variability spring predictability barrier ERSST NOAA CPC