Vortices evolution in the solar atmosphere: A dynamical equation for the swirling strength

Abstract

We study vortex dynamics in the solar atmosphere by employing and deriving the analytical evolution equations of two vortex identification criteria. The two criteria used are vorticity and the swirling strength. Vorticity can be biased in the presence of shear flows, but its dynamical equation is well known; the swirling strength is a more precise criterion for the identification of vortical flows, but its evolution equation is not known yet. Therefore, we explore the possibility of deriving a dynamical equation for the swirling strength. We then apply the two equations to analyze radiative MHD simulations of the solar atmosphere produced with the CO5BOLD code. We present a detailed review of the swirling strength criterion and the mathematical derivation of its evolution equation. This equation did not exist in the literature before and it constitutes a novel tool that is suitable for the analysis of a wide range of problems in (magneto-)hydrodynamics. By applying this equation to numerical models, we find that hydrodynamical and magnetic baroclinicities are the driving physical processes responsible for vortex generation in the convection zone and the photosphere. Higher up in the chromosphere, the magnetic terms alone dominate. Moreover, we find that the swirling strength is produced at small scales in a chaotic fashion, especially inside magnetic flux concentrations. The swirling strength represents an appropriate criterion for the identification of vortices in turbulent flows, such as those in the solar atmosphere. Moreover, its evolution equation, which is derived in this paper, is pivotal for obtaining precise information about the dynamics of these vortices and the physical mechanisms responsible for their production and evolution. Since this equation is available, the swirling strength is now the ideal quantity to study the dynamics of vortices in (magneto-)hydrodynamics.

12 pages, to be published in A&A

References in corpus (6)

• Alfven Waves in the Lower Solar Atmosphere
• Convectively driven vortex flows in the Sun
• Evidence of photospheric vortex flows at supergranular junctions observed by FG/SOT (Hinode)
• On the plasma flow inside magnetic tornadoes on the Sun
• Torsional Alfven Waves in Solar Magnetic Flux Tubes of Axial Symmetry
• Non-magnetic photospheric bright points in 3D simulations of the solar atmosphere

Cited by in corpus (7)

• The Alfvénic nature of chromospheric swirls
• A Comprehensive Radiative Magnetohydrodynamics Simulation of Active Region Scale Flux Emergence from the Convection Zone to the Corona
• An innovative and automated method for vortex identification. I. Description of the SWIRL algorithm
• New approach for analysing dynamical processes on the surface of photospheric vortex tubes
• On the influence of magnetic topology on the propagation of internal gravity waves in the solar atmosphere
• Coherent structure detection and the inverse cascade mechanism in two-dimensional Navier-Stokes turbulence
• Small-scale vortical motions in cool stellar atmospheres