Effects of MHD turbulence on mean magnetic pressure and formation of magnetic structures

A review of analytical and numerical results on effects of developed magnetohydrodynamic (MHD) turbulence on mean magnetic pressure and formation of magnetic structures is presented. Suppression of turbulent hydromagnetic pressure (the isotropic part of combined Reynolds and Maxwell stresses) by the mean large-scale magnetic field is related to an effective mechanism for the formation of magnetic inhomogeneous structures in MHD turbulence. At large Reynolds numbers and for sub-equipartition mean magnetic fields, the resulting negative turbulent contribution can be enough large so that the effective mean magnetic pressure (the sum of turbulent and non-turbulent contributions) appears negative. We also investigated the effect of mean current density on the turbulent hydromagnetic pressure reduction, and demonstrated that an enhanced mean current density increases the suppression of the turbulent pressure. Such currents are associated with sharp gradients of the growing magnetic structures. The negative effective mean magnetic pressure was found in direct numerical simulation (DNS) in both, stably stratified forced turbulence and turbulent convection. This phenomenon causes the excitation of the negative effective magnetic pressure instability (NEMPI). By the action of this instability, an initially uniform magnetic field forms flux concentrations whose scale is large compared to the turbulent scale. This instability has been recently detected in DNS of forced stratified MHD turbulence that requires enough large scale separation between the forcing scale and the size of the box (e.g., the number of turbulent eddies in the computational domain is about 30). Strong spontaneous formation of large-scale magnetic structures caused by NEMPI, is seen even without performing any spatial averaging. The characteristic time of the instability is comparable to the turbulent diffusion time. We also demonstrated that the magnetic energy of the forming large-scale inhomogeneous magnetic structures is only weakly dependent on the magnetic Reynolds number, provided its value is large enough for the excitation of NEMPI. Our DNS results support mean-field calculations and analytical results which identified this instability. For example, for an isothermal layer the onset of the instability occurs at the same depth that increases with increasing field strength, the growth rate of NEMPI is independent of the field strength, provided the magnetic structures are fully contained within the domain. NEMPI may play a crucial role in the formation of sunspots and active regions in the upper part of convective zones of Sun and stars.