The relationship between vortex flows at different spatial scales and their contribution to the energy balance in the chromosphere is not yet fully understood. We perform three-dimensional (3D) radiation-magnetohydrodynamic simulations of a unipolar solar plage region at a spatial resolution of 10 km using the MURaM code. We use the swirling-strength criterion that mainly detects the smallest vortices present in the simulation data. We additionally degrade our simulation data to smooth out the smaller vortices, so that also the vortices at larger spatial scales can be detected. Vortex flows at various spatial scales are found in our simulation data for different effective spatial resolutions. We conclude that the observed large vortices are likely clusters of much smaller ones that are not yet resolved by observations. We show that the vertical Poynting flux decreases rapidly with reduced effective spatial resolutions and is predominantly carried by the horizontal plasma motions rather than vertical flows. Since the small-scale horizontal motions or the smaller vortices carry most of the energy, the energy transported by vortices deduced from low-resolution data is grossly underestimated. In full-resolution simulation data, the Poynting flux contribution due to vortices is more than adequate to compensate for the radiative losses in plage, indicating their importance for chromospheric heating.

Context. Vortex flows exist across a broad range of spatial and temporal scales in the solar atmosphere. Small-scale vortices are thought to play an important role in energy transport in the solar atmosphere. However, their physical properties remain poorly understood due to the limited spatial resolution of the observations. Aims. We explore and analyze the physical properties of small-scale vortices inside magnetic flux tubes using numerical simulations, and investigate whether they contribute to heating the chromosphere in a plage region. Methods. Using the three-dimensional radiative magnetohydrodynamic simulation code MURaM, we perform numerical simulations of a unipolar solar plage region. To detect and isolate vortices we use the swirling strength criterion and select the locations where the fluid is rotating with an angular velocity greater than a certain threshold. We concentrate on small-scale vortices as they are the strongest and carry most of the energy. We explore the spatial profiles of physical quantities such as density and horizontal velocity inside these vortices. Moreover, to learn their general characteristics, a statistical investigation is performed. Results. Magnetic flux tubes have a complex filamentary substructure harboring an abundance of small-scale vortices. At the interfaces between vortices strong current sheets are formed that may dissipate and heat the solar chromosphere. Statistically, vortices have higher densities and higher temperatures than the average values at the same geometrical height in the chromosphere. Conclusions. We conclude that small-scale vortices are ubiquitous in solar plage regions; they are denser and hotter structures that contribute to chromospheric heating, possibly by dissipation of the current sheets formed at their interfaces.

Context. Ubiquitous vortex flows at the solar surface excite magnetohydrodynamic (MHD) waves that propagate to higher layers of the solar atmosphere. In the solar corona, these waves frequently encounter magnetic null points. The interaction of MHD waves with a coronal magnetic null in realistic 3D setups requires an appropriate wave identification method. Aims. We present a new MHD wave decomposition method that overcomes the limitations of existing wave identification methods. Our method allows for an investigation of the energy fluxes in different MHD modes at different locations of the solar atmosphere as waves generated by vortex flows travel through the solar atmosphere and pass near the magnetic null. Methods. We used the open-source MPI-AMRVAC code to simulate wave dynamics through a coronal null configuration. We applied a rotational wave driver at our bottom photospheric boundary to mimic vortex flows at the solar surface. To identify the wave energy fluxes associated with different MHD wave modes, we employed a wave decomposition method that is able to uniquely distinguish different MHD modes. Our proposed method utilizes the geometry of an individual magnetic field-line in the 3D space to separate the velocity perturbations associated with the three fundamental MHD waves. We compared our method with an existing wave decomposition method that uses magnetic flux surfaces instead. Over the selected flux surfaces, we calculated and analyzed the temporally averaged wave energy fluxes, as well as the acoustic and magnetic energy fluxes. Our wave decomposition method allowed us to estimate the relative strengths of individual MHD wave energy fluxes. Results. Our method for wave identification is consistent with previous flux-surface-based methods and provides the expected results in terms of the wave energy fluxes at various locations of the null configuration. We show that ubiquitous vortex flows excite MHD waves that contribute significantly to the Poynting flux in the solar corona. Alfvén wave energy flux accumulates on the fan surface and fast wave energy flux accumulates near the null point. There is a strong current density buildup at the spine and fan surface. Conclusions. The proposed method has advantages over previously utilized wave decomposition methods, since it may be employed in realistic simulations or magnetic extrapolations, as well as in real solar observations whenever the 3D fieldline shape is known. The essential characteristics of MHD wave propagation near a null – such as wave energy flux accumulation and current buildup at specific locations – translate to the more realistic setup presented here. The enhancement in energy flux associated with magneto-acoustic waves near nulls may have important implications in the formation of jets and impulsive plasma flows.

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.