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 $ H α , 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.

Realistic theoretical models of magnetohydrodynamic wave propagation in the different solar magnetic configurations are required to explain observational results, allowing magnetoseismology to be conducted and provide more accurate information about local plasma properties. The numerical approach described in this paper allows a dispersion diagram to be obtained for any arbitrary symmetric magnetic slab model of solar atmospheric features. This proposed technique implements the shooting method to match necessary boundary conditions on continuity of displacement and total pressure of the waveguide. The algorithm also implements fundamental physical knowledge of the sausage and kink modes such that both can be investigated. The dispersion diagrams for a number of analytic cases that model magnetohydrodynamic waves in a magnetic slab were successfully reproduced. This work is then extended by considering density structuring modelled as a series of Gaussian profiles and a sinc(x) function. A further case study investigates properties of MHD wave modes in a coronal slab with a non-uniform background plasma flow, for which the governing equations are derived. It is found that the dispersive properties of slow body modes are more greatly altered than those of fast modes when any equilibrium inhomogeneity is increased, including background flow. The spatial structure of the eigenfunctions is also modified, introducing extra nodes and points of inflexion that may be of interest to observers.

Alfvénic motions are ubiquitous in the solar atmosphere and their observed properties are closely linked to those of photospheric p-modes. However, it is still unclear how a predominantly acoustic wave driver can produce these transverse oscillations in the magnetically dominated solar corona. In this study we conduct a 3D magnetohydrodynamic numerical simulation to model a straight, expanding coronal loop in a gravitationally stratified solar atmosphere which includes a transition region and chromosphere. We implement a driver locally at one foot-point corresponding to an acoustic–gravity wave which is inclined by θ = 15° with respect to the vertical axis of the magnetic structure and is equivalent to a vertical driver incident on an inclined loop. We show that transverse motions are produced in the magnetic loop, which displace the axis of the waveguide due to the breaking of azimuthal symmetry, and study the resulting modes in the theoretical framework of a magnetic cylinder model. By conducting an azimuthal Fourier analysis of the perturbed velocity signals, the contribution from different cylindrical modes is obtained. Furthermore, the perturbed vorticity is computed to demonstrate how the transverse motions manifest themselves throughout the whole non-uniform space. Finally we present some physical properties of the Alfvénic perturbations and present transverse motions with velocity amplitudes in the range 0.2–0.75 km s−1 which exhibit two distinct oscillation regimes corresponding to 42 and 364 s, where the latter value is close to the period of the p-mode driver in the simulation.

Magnetohydrodynamic (MHD) waves are routinely observed in the solar atmosphere. These waves are important in the context of solar physics as it is widely believed they can contribute to the energy budget of the solar atmosphere and are a prime candidate to contribute towards coronal heating. Realistic models of these waves are required representing observed configurations such that plasma properties can be determined more accurately which can not be measured directly. This work utilises a previously developed numerical technique to find permittable eigenvalues under different non-uniform equilibrium conditions in a Cartesian magnetic slab geometry. Here we investigate the properties of magnetoacoustic waves under non-uniform equilibria in a cylindrical geometry. Previously obtained analytical results are retrieved to emphasise the power and applicability of this numerical technique. Further case studies investigate the effect that a radially non-uniform plasma density and non-uniform plasma flow, modelled as a series of Gaussian profiles, has on the properties of different MHD waves. For all cases the dispersion diagrams are obtained and spatial eigenfunctions calculated which display the effects of the equilibrium inhomogeneity. It is shown that as the equilibrium non-uniformity is increased, the radial spatial eigenfunctions are affected and extra nodes introduced, similar to the previous investigation of a magnetic slab. Furthermore, azimuthal perturbations are increased with increasing inhomogeneity introducing vortical motions inside the waveguide. Finally, 2D and 3D representations of the velocity fields are shown which may be useful for observers for wave mode identification under realistic magnetic waveguides with ever increasing instrument resolution.