Super-diffusion versus competitive advection: a simulation

TL;DR

This study investigates the super-diffusive behavior of magnetic elements on the solar surface, demonstrating through data analysis and simulation that competitive advection alone can produce super-diffusion without requiring fully developed turbulence.

Contribution

The paper introduces a simulation of passive tracers in a Voronoi network showing that super-diffusive displacement spectra can arise from competitive advection, challenging the turbulence hypothesis.

Findings

Super-diffusive regime observed in both data-sets and simulation.

Competitive advection can reproduce super-diffusive signatures.

Turbulence is not necessary to explain magnetic element motion.

Abstract

Magnetic element tracking is often used to study the transport and diffusion of the magnetic field on the solar photosphere. From the analysis of the displacement spectrum of these tracers, it has been recently agreed that a regime of super-diffusivity dominates the solar surface. Quite habitually this result is discussed in the framework of fully developed turbulence. But the debate whether the super-diffusivity is generated by a turbulent dispersion process, by the advection due to the convective pattern, or by even another process, is still open, as is the question about the amount of diffusivity at the scales relevant to the local dynamo process. To understand how such peculiar diffusion in the solar atmosphere takes places, we compared the results from two different data-sets (ground-based and space-borne) and developed a simulation of passive tracers advection by the deformation of a Voronoi network. The displacement spectra of the magnetic elements obtained by the data-sets are consistent in retrieving a super-diffusive regime for the solar photosphere, but the simulation also shows a super-diffusive displacement spectrum: its competitive advection process can reproduce the signature of super-diffusion. Therefore, it is not necessary to hypothesize a totally developed turbulence regime to explain the motion of the magnetic elements on the solar surface.