Can cellular convection in a rotating spherical shell maintain both   global and local magnetic fields?
  A convection-driven MHD dynamo in a rotating spherical shell, with clearly defined structural elements in the flow and magnetic field, is simulated numerically. Such dynamos can be called deterministic, in contrast to those explicitly dependent on the assumed properties of turbulence. The cases most interesting from the standpoint of studying the nature of stellar magnetism demonstrate the following features. On a global scale, the convective flows can maintain a ``general'' magnetic field with a sign-alternating dipolar component. Local (in many cases, bipolar) magnetic structures are associated with convection cells. Disintegrating local structures change into background fields, which drift toward the poles. From time to time, reversals of the magnetic fields in the polar regions occur, as ``new'' background fields expel the ``old'' fields. 
A.V. Getling, R.D. Simitev, and F.H. Busse