Vortex flows, related to solar convective turbulent dynamics at granular scales and their interplay with magnetic fields within intergranular lanes, occur abundantly on the solar surface and in the atmosphere above. Their presence is revealed in high-resolution and high-cadence solar observations from the ground and from space and with state-of-the-art magnetoconvection simulations. Vortical flows exhibit complex characteristics and dynamics, excite a wide range of different waves, and couple different layers of the solar atmosphere, which facilitates the channeling and transfer of mass, momentum and energy from the solar surface up to the low corona. Here we provide a comprehensive review of documented research and new developments in theory, observations, and modelling of vortices over the past couple of decades after their observational discovery, including recent observations in $\text{H}\alpha $Hα , innovative detection techniques, diverse hydrostatic modelling of waves and forefront magnetohydrodynamic simulations incorporating effects of a non-ideal plasma. It is the first systematic overview of solar vortex flows at granular scales, a field with a plethora of names for phenomena that exhibit similarities and differences and often interconnect and rely on the same physics. With the advent of the 4-m Daniel K. Inouye Solar Telescope and the forthcoming European Solar Telescope, the ongoing Solar Orbiter mission, and the development of cutting-edge simulations, this review timely addresses the state-of-the-art on vortex flows and outlines both theoretical and observational future research directions.

Torsional oscillations represent bands of fast and slow zonal flows around the Sun, which extend deep into the convection zone and migrate during solar cycles toward the equator following the sunspot “butterfly” diagram. Analysis of helioseismology data obtained in 1996–2018 for almost two solar cycles reveals zones of deceleration of the torsional oscillations inside of the Sun due to dynamo-generated magnetic field. The zonal deceleration originates near the bottom of the convection zone at high latitudes, and migrates to the surface revealing patterns of magnetic dynamo waves predicted by Parker’s dynamo theory. The analysis reveals that the primary seat of the solar dynamo is located in a high-latitude zone of the tachocline. It suggests a dynamo scenario that can explain “extended solar cycles” previously observed in the evolving shape of the solar corona. The results show a substantial decrease of the zonal acceleration in the current solar cycle and indicate a further decline of activity in the next solar cycle. Although the relationship between the magnitude of zonal deceleration and the amount of emerged toroidal field that leads to formation of sunspots is not yet established, the results reveal a new perspective for solar cycle modeling and prediction using helioseismology data.

The phenomenon of solar “torsional oscillations” (TO) represents migratory zonal flows associated with the solar cycle. These flows are observed on the solar surface and, according to helioseismology, extend through the convection zone. We study the origin of the TO using results from a global MHD simulation of the solar interior that reproduces several of the observed characteristics of the mean-flows and magnetic fields. Our results indicate that the magnetic tension (MT) in the tachocline region is a key factor for the periodic changes in the angular momentum transport that causes the TO. The torque induced by the MT at the base of the convection zone is positive at the poles and negative at the equator. A rising MT torque at higher latitudes causes the poles to speed up, whereas a declining negative MT torque at the lower latitudes causes the equator to slow-down. These changes in the zonal flows propagate through the convection zone up to the surface. Additionally, our results suggest that it is the magnetic field at the tachocline that modulates the amplitude of the surface meridional flow rather than the opposite as assumed by flux-transport dynamo models of the solar cycle.

Two fundamental properties of stellar magnetic fields have been determined by observations for solar-like stars with different Rossby numbers ( ), namely, the magnetic field strength and the magnetic cycle period. The field strength exhibits two regimes: (1) for fast rotation, it is independent of , and (2) for slow rotation, it decays with following a power law. For the magnetic cycle period, two regimes of activity, the active and inactive branches, have also been identified. For both of them, the longer the rotation period, the longer the activity cycle. Using global dynamo simulations of solar-like stars with Rossby numbers between ∼0.4 and ∼2, this paper explores the relevance of rotational shear layers in determining these observational properties. Our results, consistent with nonlinear dynamos, show that the total magnetic field strength is independent of the rotation period. Yet at surface levels, the origin of the magnetic field is determined by . While for , it is generated in the convection zone, for , strong toroidal fields are generated at the tachocline and rapidly emerge toward the surface. In agreement with the observations, the magnetic cycle period increases with the rotational period. However, a bifurcation is observed for , separating a regime where oscillatory dynamos operate mainly in the convection zone from the regime where the tachocline has a predominant role. In the latter, the cycles are believed to result from the periodic energy exchange between the dynamo and the magneto-shear instabilities developing in the tachocline and the radiative interior.

We present a nonlinear mean-field model of the solar interior dynamics and dynamo, which reproduces the observed cyclic variations of the global magnetic field of the Sun, as well as the differential rotation and meridional circulation. Using this model, we explain, for the first time, the extended 22 yr pattern of the solar torsional oscillations, observed as propagation of zonal variations of the angular velocity from high latitudes to the equator during the time equal to the full dynamo cycle. In the literature, this effect is usually attributed to the so-called “extended solar cycle.” In agreement with the commonly accepted idea, our model shows that the torsional oscillations can be driven by a combination of magnetic field effects acting on turbulent angular momentum transport and the large-scale Lorentz force. We find that the 22 yr pattern of the torsional oscillations can result from a combined effect of an overlap of subsequent magnetic cycles and magnetic quenching of the convective heat transport. The latter effect results in cyclic variations of the meridional circulation in the sunspot formation zone, in agreement with helioseismology results. The variations of the meridional circulation, together with other drivers of the torsional oscillations, maintain their migration to the equator during the 22 yr magnetic cycle, resulting in the observed extended pattern of the torsional oscillations.