ABSTRACT
In this chapter, we focus on the effects of nonlinearity. After general considerations in Section 2.1, we investigate the role of nonlinearity in saturating the growth of the magnetic field for a dynamo with a spatially periodic flow in Section 2.2. We then turn to the more general situation of saturation in the vicinity of the dynamo threshold; first in the low Re limit in Section 2.3 and then in the high Re limit in Section 2.4. We then address the issue of dynamo saturation in flows strongly affected by rotation (with planetary applications in mind) in Section 2.5, and we present some conjectures for the magnetic field generated by a turbulent flow when Re and Rm are both large in Section 2.6. Mean field dynamo saturation (with astrophysical applications in mind) is discussed in Section 2.7. Finally, we return in Section 2.8 to the apparently simple disc dynamo model used as an introductory example in Chapter 1 to show how rich the nonlinear dynamical behaviour can be.
