We study the solar-cycle variation of the divergence and vorticity of subsurface horizontal flows from the surface to a depth of 16 Mm. The flows were derived with ring-diagram analysis applied to Michelson Doppler Imager (MDI) Dynamics Program, Global Oscillation Network Group (GONG), and Helioseismic and Magnetic Imager (HMI) Dopplergrams. We study their variation for the complete data set and for two subsets representing active and quiet regions. All three data sets show alternating bands of diverging and converging flows and bands of cyclonic and anticyclonic flows moving from mid-latitudes toward the equator during a solar cycle. For Solar Cycle 24, these bands are precursors of the magnetic activity appearing several years before magnetic activity is present at a given latitude even leading the fast bands of the flows. The amplitude differences between the cyclonic and anticyclonic and the converging and diverging bands during a solar cycle agree within the error bars between the complete data set and the two subsets. For Solar Cycle 24, the amplitude differences are \(6.0 \pm 0.7 \;10^{-8}~\text{s}^{-1}\) for the bands of vorticity and \(-4.9 \pm 0.6\;10^{-8}~\text{s}^{-1}\) for those of divergence averaged over 2.0 – 11.6 Mm using the complete data set. The amplitude differences of Solar Cycle 23 are \(26 \pm 3\)% smaller than those of Solar Cycle 24. The flows of the active-region subset are more converging and cyclonic than those of the quiet-region subset with an extra vorticity of \(1.3 \pm 0.1 \;10^{-8}~\text{s}^{-1}\) and an extra divergence of \(-6.7 \pm 0.3\;10^{-8}~\text{s}^{-1}\) averaged over 7.5^∘ – 30^∘ and all depths and epochs. The amplitude of the extra divergence of active regions is about a factor of 1.3 larger at depths shallower than 6 Mm and decreases with increasing depth, while the extra vorticity is nearly constant with depth.

我们研究了从表面到深度为16 Mm的地下水平流的发散度和涡度的太阳周期变化。这些流量是通过应用于迈克尔逊多普勒成像仪（MDI）动力学程序，全球振荡网络组（GONG）以及日震和磁成像仪的环形图分析得出的（HMI）多谱图。我们针对完整的数据集以及代表活动区域和安静区域的两个子集研究了它们的变化。所有这三个数据集显示了在太阳周期期间从中纬度向赤道移动的发散和会聚流的交替带以及气旋和反气旋流的带。对于太阳周期24，这些带是磁活动出现的前兆，而磁活动在给定纬度下甚至领先于流动的快速带之前就已经出现了好几年。太阳周期中气旋和反气旋以及会聚和发散频带之间的振幅差在完整数据集和两个子集之间的误差线内一致。对于太阳周期24，振幅差为\（6.0 \ pm 0.7 \; 10 ^ {-8}〜\ text {s} ^ {-1} \）使用完整的数据集，涡度带为\（-4.9 \ pm 0.6 \; 10 ^ {-8}〜\ text {s} ^ {-1} \）的带平均为2.0 – 11.6 Mm。太阳周期23的振幅差比太阳周期24的小（\ 26 \ pm 3 \）％。活动区域子集的流动比安静区域子集的流动更具收敛性和气旋性，且具有额外的涡度的\（1.3 \ PM 0.1 \; 10 ^ { - 8}〜\文本{S} ^ { - 1} \）和额外的发散\（ - 6.7 \ PM 0.3 \; 10 ^ { - 8}〜\文本{S} ^ { - 1} \）平均超过7.5 ^∘  - 30 ^∘以及所有的深度和时代。有源区额外发散的幅度在小于6 Mm的深度处大约大1.3倍，并且随深度增加而减小，而额外涡度随深度几乎恒定。