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.

我们将带有四个耦合振荡器的 Kuramoto 模型应用于描述不同纬度的太阳磁场代理的相位演变。我们表明，一个由四个耦合振荡器组成的环确实代表了子午环流的频率同步和太阳代理的相位演变。该模型允许人们重建不同纬度的经向流速和半球不对称性的长期演变。我们研究了子午流的 NS 不对称性，并发现了自然频率和耦合的百年变化。近赤道子午流的南北不对称的极端对应于太阳周期 (SC)19-20 和 SC23-24 中太阳活动的异常。我们还发现 SC23-24 中经向环流环轮廓的退化，这与日震观测一致。我们表明 NS 不对称性取决于纬度，并且与近赤道子午线流密切相关。