Dynamics of Large-Scale Solar Flows

Abstract

The Sun's axisymmetric large-scale flows, differential rotation and meridional circulation, are thought to be maintained by the influence of rotation on the thermal-convective motions in the solar convection zone. These large-scale flows are crucial for maintaining the Sun's global magnetic field. Over the last several decades, our understanding of large-scale motions in the Sun has significantly improved, both through observational and theoretical efforts. Helioseismology has constrained the flow topology in the solar interior, and the growth of supercomputers has enabled simulations that can self-consistently generate large-scale flows in rotating spherical convective shells. In this article, we review our current understanding of solar convection and the large-scale flows present in the Sun, including those associated with the recently discovered inertial modes of oscillation. We discuss some issues still outstanding, and provide an outline of future efforts needed to address these.

Keywords: Convection; Differential rotation; Helioseismology; Meridional flow; Numerical simulation.

Fig. 1

Internal profile of the solar differential rotation deduced from global helioseismology and averaged from April 2010 to February 2021. Panels (a) and (b) show the results obtained by the Global Oscillation Network Group (GONG) (data courtesy of R. Howe, using the method of Howe et al. 2005) and the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) (Larson and Schou 2018). Panel (c) shows the radial differential rotation at selected latitudes. Grey shades denote the layers of strong radial rotational shear known as the tachocline and the near-surface shear layer (NSSL)

Fig. 2

Latitudinal component of the meridional flow inferred by time-distance local helioseismology. The red and blue shades correspond to the northward and southward directions respectively. (a) The result obtained by Zhao et al. (2013) using SDO/HMI data (2010–2012), reproduced with permission. (b) The result obtained by Gizon et al. (2020a) using GONG data (2008–2019), reprinted with permission from AAAS

Fig. 3

From Hathaway et al. (2015): Solar Doppler velocity spectrum as determined from Helioseismic and Magnetic Imager (HMI) observations (red curves, with and without removal of image artifacts), along with a random-phase synthetic spectrum (black curve). Vertical blue dashed fiducial lines have been added indicating the approximate scale of supergranulation and giant-cells. The blue dotted line approximately over-plots the spectrum seen in numerical simulations. Figure without added dashed and dotted blue lines used with permission of Hathaway et al. (2015)

Fig. 4

Observational power spectra in the Carrington frame and eigenfunctions of three selected inertial modes of the Sun. Top row: Power spectra of the longitudinal component of velocity $u_{\varphi }$ for $m=1$ (left column) and $m=2$ (middle column), and power spectrum of the colatitudinal component of velocity $u_{\theta }$ for $m=3$. The blue curves show the differential rotation rate at $r=0.96R_{\odot }$ and $R_{\odot }$. The purple contour indicates the region affected by active-region flows. Middle row: The same power spectra but normalized at each latitude by their average value over the frequency range between the orange bars. Excess power is seen at a specific frequency at all latitudes in each of the three cases. The red arrows point to critical latitudes at the surface for the case $m=2$. Bottom row: Observed horizontal velocity eigenfunctions at the surface for the $m=1$ high-latitude mode, the $m=2$ critical-latitude mode, and the $m=3$ equatorial Rossby mode. These figures are courtesy of Gizon et al. (2021)

Fig. 5

Horizontal velocity power spectra near the solar surface. (a) Comparison of the spectra between numerical simulations and the observations at $r=0.96R_{\odot }$ (Birch 2023). Blue: A global full-spherical simulation of rotating magneto-convection by Hotta and Kusano (2021). Navy: A local cartesian box simulation of solar convection by Hotta et al. (2019). Black (gray area): Observational upper limits inferred by deep-focusing time-distance helioseismic measurement of Hanasoge et al. (2012), revised recently by Proxauf (2020). (b) Comparison of the spectra obtained by various observational measurements at various depths. Red: Multi-ridge fitting ring-diagram analysis by Greer et al. (2015), revised recently by Nagashima et al. (2020). Green: Local correlation tracking of surface granulation (Proxauf 2020). Magenta: The SDO/HMI ring-diagram pipeline (Bogart et al. ,; Proxauf 2020). All observations reported in the above plots are available online (Birch 2023)