North–South Asymmetry of Solar Meridional Circulation and Synchronization: Two Rings of Four Coupled Oscillators

We apply the Kuramoto model with four coupled oscillators to the description of the phase evolution of solar magnetic field proxies at different latitudes. We show that a ring of four coupled oscillators does represent the frequency synchronization of the meridional circulation and the phase evolution of solar proxies. The model allows one to reconstruct the long-term evolution of the meridional flow speed and hemispheric asymmetry at different latitudes. We study the N-S asymmetry of the meridional flow and find a centennial variation of natural frequencies and couplings. Extremes of the north–south asymmetry of the near-equatorial meridional flow correspond to the anomalies of solar activity in Solar Cycles (SC)19–20 and SC23–24. We also find a degeneration of the meridional circulation ring profile in SC23–24, which agrees with helioseismic observations. We show that the N-S asymmetry depends on latitude and is strongly connected with the near-equatorial meridional flow.