  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 be converged 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.
