Vortex tube formation in solar turbulent convection

Turbulent solar convection is a source of various processes observed as large-scale active phenomena, e.g., coronal mass ejections, formation of self-organized magnetic structures that appear on the surface as sunspots and pores, and other non-linear dynamical structures and phenomena. Modern realistic numerical simulations of solar turbulent phenomena are based on first physical principles and take into account the real-gas equation of state, radiative transfer, chemical composition, and effects of magnetic fields. The physical description of the dynamical properties of solar convection can be improved through implementation of subgrid-scale turbulence models, which make numerical models more realistic and allow us to resolve essential physical scales. This approach has demonstrated good agreement of numerical modeling results with observations (e.g. Jacoutot et al. 2008). Realistic 3D numerical simulations have also reproduced and explained many observed effects in sunspots and magnetic active regions (e.g., Kitiashvili et al. 2009, 2010; Rempel et al. 2011; Stein et al. 2011), and in quiet-Sun regions (Stein & Nordlund 2000; Steiner et al. 2010; Kitiashvili et al. 2011). Thus, the numerical simulations provide important insights into the physical mechanisms of solar phenomena. Vorticity is one of the basic properties of turbulent flows. Therefore it is not surprising that swirling motions are found in observations of the highly-turbulent solar magnetoconvection. Large-scale vortical behavior, once evidenced by sunspot rotation, was first observed on the Sun by Secchi (1857). Later, vortex flows in the photosphere (∼ 3 Mm in diameter) were detected by Brandt et al. (1988), and small-scale swirling flows (∼ 0.5 Mm) were observed by Wang et al. (1995). Recent observations have shown that vortices are ubiquitous in non-magnetic quiet-Sun regions (Pötzi & Brandt 2005; Bonet et al. 2008, 2010). Such swirling motions correspond to vertically oriented vortex tube structures that were found in numerical simulations (e.g., Brandenburg et al. 1996; Stein & Nordlund 2000; Kitiashvili et al. 2011). Both observations and simulations have shown that vortex tubes play a fundamental role in solar flux dynamics. Also, recently, small-scale horizontal vortex tubes located along granule edges were found both in numerical simulations and in observations with the balloon observatory SUNRISE (Steiner et al. 2010). However, even the highest resolution observations are not capable of resolving the structure of the vortex tubes. Thus it is important to investigate in detail the mechanism of their formation and dynamics using high-resolution numerical simulations. Vortex tube formation can occur from several different mechanisms. According to our numerical simulations, vertical vortex-tube generation on the Sun can be driven