A dynamo is a mechanism for converting flow energy to magnetic energy. The magnetic fields of most stars and galaxies are probably sustained by dynamos. The flow energy has an ordered component - the large scale differential rotation, and a turbulent component. Both are important.
The solar dynamo, and some stellar dynamos, are cyclic in time, with the cycle period of the solar dynamo being 22 years, and other cycles being observed on many different stars. One way to study stellar dynamos is through numerical simulations. The accompanying figure shows a "magnetic wreath" prodiced by one of Ben Brown's dynamo simulations. The magnetic field is stretched by rotation into a ring in a plane perpendicular to the rotation axis. Eventually we would like to understand the relationship between stellar rotation, luminosity, and the length and vigor of its magnetic cycles.
Dynamos can also be studied in the laboratory. There are two dynamo experiments at UW-Madison. The Madison Dynamo Experiment is a ball of liquid sodium that can be mechanically stirred. The Madison Plasma Dynamo Experiment will be a ball of plasma that can be used to to study a host of dynamo problems, inlcuding some related to the growth of magnetic fields in the early universe.