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.

Solar chromospheric observations of sunspot umbrae offer an exceptional view of magnetohydrodynamic wave phenomena. In recent years, a wealth of wave signatures related to propagating magneto-acoustic modes have been presented, which demonstrate complex spatial and temporal structuring of the wave components. Theoretical modeling has demonstrated how these ubiquitous waves are consistent with an m = 0 slow magneto-acoustic mode, which is excited by trapped sub-photospheric acoustic (p-mode) waves. However, the spectrum of umbral waves is broad, suggesting that the observed signatures represent the superposition of numerous frequencies and/or modes. We apply Fourier filtering, in both spatial and temporal domains, to extract chromospheric umbral wave characteristics consistent with an m = 1 slow magneto-acoustic mode. This identification has not been described before. Angular frequencies of 0.037 ± 0.007 rad s − 1 ( 2.1 ± 0.4 deg s − 1 , corresponding to a period ≈170 s) for the m = 1 mode are uncovered for spatial wavenumbers in the range of 0.45 < k < 0.90 arcsec⁻¹ (5000−9000 km). Theoretical dispersion relations are solved, with corresponding eigenfunctions computed, which allows the density perturbations to be investigated and compared with our observations. Such magnetohydrodynamic modeling confirms our interpretation that the identified wave signatures are the first direct observations of an m = 1 slow magneto-acoustic mode in the chromospheric umbra of a sunspot.