Nonlinear dynamo theory

Using the asymptotic method of multiple scales construct nonlinear theory of large-scale structures in stratified conducting medium in the presence of small-scale oscillations of the velocity field and magnetic fields. Such small-scale stationary oscillations are generated by small external sources at low Reynolds numbers. The nonlinear system of equations describing the evolution of largescale structure of the velocity field and the magnetic fields are obtained. The linear stage of evolution leads to the well known instability. We study the equations of non-linear instability and its stationary solutions.