A nonlinear electromotive force for an anisotropic turbulence in the case of intermediate nonlinearity is derived. The intermediate nonlinearity implies that the mean magnetic field is not strong enough to affect the correlation time of a turbulent velocity field. The nonlinear mean-field dependencies of the hydrodynamic and magnetic parts of the $\alpha$ effect, turbulent diffusion, and turbulent diamagnetic and paramagnetic velocities for an anisotropic turbulence are found. It is shown that the nonlinear turbulent diamagnetic and paramagnetic velocities are determined by both an inhomogeneity of the turbulence and an inhomogeneity of the mean magnetic field $\mathbf{B}.$ The latter implies that there are additional terms in the turbulent diamagnetic and paramagnetic velocities $\propto \mathbf{\nabla }{B}^2$ and $\propto \left(\mathbf{B}\cdot \mathbf{\nabla }\right)\mathbf{B}.$ These effects are caused by a tangling of a nonuniform mean magnetic field by hydrodynamic fluctuations. This increases the inhomogeneity of the mean magnetic field. It is also shown that in an isotropic turbulence the mean magnetic field causes an anisotropy of the nonlinear turbulent diffusion. Two types of nonlinearities in magnetic dynamo determined by algebraic and differential equations are discussed. Nonlinear systems of equations for axisymmetric $\alpha \Omega$ dynamos in both spherical and cylindrical coordinates are derived.

• Received 19 May 1999

DOI:https://doi.org/10.1103/PhysRevE.61.5202