  Strongly stratified hydromagnetic turbulence has previously been found to
produce magnetic flux concentrations if the domain is large enough compared
with the size of turbulent eddies. Mean-field simulations (MFS) using
parameterizations of the Reynolds and Maxwell stresses show a negative
effective magnetic pressure instability and have been able to reproduce many
aspects of direct numerical simulations (DNS) regarding the growth rate of this
large-scale instability, shape of the resulting magnetic structures, and their
height as a function of magnetic field strength. Unlike the case of an imposed
horizontal field, for a vertical one, magnetic flux concentrations of
equipartition strength with the turbulence can be reached. This results in
magnetic spots that are reminiscent of sunspots. Here we want to find out under
what conditions magnetic flux concentrations with vertical field occur and what
their internal structure is. We use a combination of MFS, DNS, and implicit
large-eddy simulations to characterize the resulting magnetic flux
concentrations in forced isothermal turbulence with an imposed vertical
magnetic field. We confirm earlier results that in the kinematic stage of the
large-scale instability the horizontal wavelength of structures is about 10
times the density scale height. At later times, even larger structures are
being produced in a fashion similar to inverse spectral transfer in helically
driven turbulence. Using turbulence simulations, we find that magnetic flux
concentrations occur for different values of the Mach number between 0.1 and
0.7. DNS and MFS show magnetic flux tubes with mean-field energies comparable
to the turbulent kinetic energy. The resulting vertical magnetic flux tubes are
being confined by downflows along the tubes and corresponding inflow from the
sides, which keep the field concentrated.
