The negative effective magnetic pressure in stratified forced turbulence

Axel Brandenburg, Koen Kemel, Nathan Kleeorin, Igor Rogachevskii

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


To understand the basic mechanism of the formation of magnetic flux concentrations, we determine by direct numerical simulations the turbulence contributions to the mean magnetic pressure in a strongly stratified isothermal layer with large plasma beta, where a weak uniform horizontal mean magnetic field is applied. The negative contribution of turbulence to the effective mean magnetic pressure is determined for strongly stratified forced turbulence over a range of values of magnetic Reynolds and Prandtl numbers. Small-scale dynamo action is shown to reduce the negative effect of turbulence on the effective mean magnetic pressure. However, the turbulence coefficients describing the negative effective magnetic pressure phenomenon are found to converge for magnetic Reynolds numbers between 60 and 600, which is the largest value considered here. In all these models, the turbulent intensity is arranged to be nearly independent of height, so the kinetic energy density decreases with height due to the decrease in density. In a second series of numerical experiments, the turbulent intensity increases with height such that the turbulent kinetic energy density is nearly independent of height. Turbulent magnetic diffusivity and turbulent pumping velocity are determined with the test-field method for both cases. The vertical profile of the turbulent magnetic diffusivity is found to agree with what is expected based on simple mixing length expressions. Turbulent pumping is shown to be down the gradient of turbulent magnetic diffusivity, but it is twice as large as expected. Corresponding numerical mean-field models are used to show that a large-scale instability can occur in both cases, provided the degree of scale separation is large enough and hence the turbulent magnetic diffusivity small enough.

Original languageEnglish
Article number179
JournalAstrophysical Journal
Issue number2
StatePublished - 20 Apr 2012


  • magnetic fields
  • magnetohydrodynamics (MHD)
  • sunspots
  • turbulence

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


Dive into the research topics of 'The negative effective magnetic pressure in stratified forced turbulence'. Together they form a unique fingerprint.

Cite this