[Paper Review] Vortices evolution in the solar atmosphere: A dynamical equation for the swirling strength

J. R. Canivete Cuissa, O. Steiner|arXiv (Cornell University)|May 26, 2020

Solar and Space Plasma Dynamics35 references4 citations

TL;DR

This paper derives the first analytical evolution equation for swirling strength—a more accurate vortex identification criterion than vorticity in turbulent flows—applying it to radiative MHD simulations of the solar atmosphere. The key contribution is identifying hydrodynamic and magnetic baroclinicities as dominant drivers of vortex generation in the convection zone and photosphere, with magnetic terms alone dominating in the chromosphere, where swirling strength is produced chaotically at small scales within magnetic flux concentrations.

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.

Motivation & Objective

• To address the limitation of vorticity as a vortex identification criterion in turbulent solar flows due to shear flow bias.
• To develop a robust, physically grounded alternative criterion for vortex detection using swirling strength.
• To derive the first analytical evolution equation for swirling strength in (magneto-)hydrodynamics.
• To apply this equation to radiative MHD simulations to identify the dominant physical mechanisms driving vortex formation and evolution in the solar atmosphere.
• To enable more accurate dynamical analysis of vortices in solar plasma, particularly in the context of magnetic tornadoes and energy transport.

Proposed method

• Derive the evolution equation for swirling strength using the momentum equation and velocity gradient tensor decomposition.
• Apply the derived equation to 3D radiative MHD simulations generated with the CO 5 BOLD code.
• Use the velocity field and magnetic field data from simulations to compute all terms in the swirling strength equation at each spatial point and time step.
• Analyze the spatial distribution and relative importance of source terms (e.g., baroclinic, magnetic tension) in different atmospheric layers.
• Visualize horizontal cross-sections of the swirling strength equation terms at three characteristic heights to reveal spatial patterns and scale structures.
• Compare the dynamics of swirling strength with vorticity to assess the reliability of vortex identification and the role of shear flows.

Experimental results

Research questions

• RQ1 What physical mechanisms are primarily responsible for the generation of swirling strength in the solar convection zone and photosphere?
• RQ2 How does the production of swirling strength differ from that of vorticity in terms of dominant source terms?
• RQ3 To what extent do magnetic baroclinic and magnetic tension terms contribute to the evolution of swirling strength in the chromosphere?
• RQ4 Where in the solar atmosphere is swirling strength produced most intensely, and what is the spatial structure of its production?
• RQ5 Can the swirling strength criterion detect vortices in turbulent, magnetic environments more reliably than vorticity?

Key findings

• Hydrodynamic and magnetic baroclinicities are the dominant physical processes driving the production of vertical swirling strength in the convection zone and photosphere.
• In the chromosphere, magnetic terms alone dominate the production of swirling strength, with a more isotropic and widespread distribution compared to the photosphere.
• Swirling strength is produced at small scales in a chaotic, patchy fashion, especially within magnetic flux concentrations.
• The production of swirling strength often involves opposing contributions from hydrodynamic and magnetic baroclinic terms, which can cancel each other locally.
• Magnetic tension and magnetic baroclinicity contribute equally to the evolution of swirling strength in the chromosphere, unlike in vorticity dynamics where tension dominates.
• The spatial structure of swirling strength production reveals small-scale, opposite-orientation patches, suggesting possible links to turbulent motions or torsional Alfvén waves.