https://stockholmuniversity.zoom.us/j/940229961
Nonlinear mean-field dynamo theories take into account algebraic and dynamic quenching of alpha effect and algebraic quenching of turbulent magnetic diffusivity. However, the theories of the algebraic quenching do not take into account the effect of modification of the source of turbulence by the growing large-scale magnetic field. This phenomenon is due to the dissipation of the strong large-scale magnetic field resulting in an increase of the total turbulent energy. This effect has been studied using the budget equation for the total turbulent energy (which takes into account the feedback of the generated large-scale magnetic field on the background turbulence). As the result of this effect, a nonlinear dynamo number decreases with increase of the large-scale magnetic field, so that that the mean-field dynamo instabilities are always saturated by the strong large-scale magnetic field. Effects of fast rotation on a density stratified turbulent convection is discussed as well. In particular, we consider a mean-field theory of differential rotation and generation of large-scale vorticity in a density stratified rotating turbulent convection. The theory takes into account a combined effect of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. The used model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with increase of the rotation rate. Applications to the solar and stellar dynamos as well as formation of large spots observed as immense storms in great planets (e.g., the Great Red Spot in Jupiter and large spots in Saturn) are discussed.