Large‐scale magnetic flux concentrations from turbulent stresses

Abstract

In this study we provide the first numerical demonstration of the effects of turbulence on the mean Lorentz force and the resulting formation of large-scale magnetic structures. Using three-dimensional direct numerical simulations (DNS) of forced turbulence we show that an imposed mean magnetic field leads to a decrease of the turbulent hydromagnetic pressure and tension. This phenomenon is quantified by determining the relevant functions that relate the sum of the turbulent Reynolds and Maxwell stresses with the Maxwell stress of the mean magnetic field. Using such a parameterization, we show by means of two-dimensional and three-dimensional mean-field numerical modelling that an isentropic density stratified layer becomes unstable in the presence of a uniform imposed magnetic field. This large-scale instability results in the formation of loop-like magnetic structures which are concentrated at the top of the stratified layer. In three dimensions these structures resemble the appearance of bipolar magnetic regions in the Sun. The results of DNS and mean-field numerical modelling are in good agreement with theoretical predictions. We discuss our model in the context of a distributed solar dynamo where active regions and sunspots might be rather shallow phenomena.

Properties of the negative effective magnetic pressure instability

“…Recently, direct numerical simulations (DNS) of both unstratified and stratified forced turbulence (Brandenburg et al 2010; hereafter referred to as BKR and BKKR, respectively) have substantiated this idea and have demonstrated that the effective magnetic pressure can indeed change sign. Similar results have now also been obtained for turbulent convection (Käpylä et al 2012).…”

Cycles and cycle modulations

“…A positive value of q s (but with large error bars) was originally reported for unstratified turbulence (Brandenburg et al 2010). Later, stratified simulations with isothermal stable stratification ) and convectively unstable stratification (Käpylä et al 2012) showed that it is small and negative.…”

“…The fact that this phenomenon can lead to an instability in a stratified layer was first found in mean-field models (Brandenburg et al 2010Käpylä et al 2012), and more recently in DNS . However, NEMPI has not yet been able to explain flux concentration in the direction along the mean magnetic field, i.e., the largescale structures remain essentially axisymmetric.…”

Surface flux concentrations in a sphericalα2dynamo

“…We therefore adopted a simple α quenching prescription to arrange the field strength to be in the desired range. Furthermore, unlike much of the earlier work on NEMPI, we used an adiabatic stratification here instead of an isothermal one; see Brandenburg et al (2010) and Käpylä et al (2012) for earlier examples with adiabatic stratification in Cartesian geometry. An adiabatic stratification implies that the pressure scale height is no longer constant and now much shorter in the upper layers than in the bulk of the domain.…”

“…Direct numerical simulations (DNS; see Brandenburg et al 2011;Kemel et al 2012a), mean-field simulations (MFS; see Brandenburg et al 2010Brandenburg et al , 2012Kemel et al 2012b;Käpylä et al 2012), and earlier analytic studies (Kleeorin et al 1989(Kleeorin et al , 1990(Kleeorin et al , 1996Kleeorin & Rogachevskii 1994;Rogachevskii & Kleeorin 2007) now provide conclusive evidence for the physical reality of NEMPI. However, open questions still need to be answered before it can be applied to detailed models of active regions and sunspot formation.…”