Essentially nonlinear dynamos

Nic Brummell, UC Santa Cruz
March 20th, 2013 at 4PM–5PM in 939 Evans Hall [Map]

The origin of magnetic fields in cosmological bodies is often attributed to the expected presence of dynamo action, where magnetic fields are amplified and sustained against dissipative processes. It is expected that any sufficiently turbulent flow in an electrically conducting fluid is likely to be able to sustain a dynamo on the scales of the velocity field, but producing magnetic field on scales much larger than those of the velocity is a much more difficult problem. However, this situation typifies the astrophysical situation: the solar magnetic activity cycle is a classic example. Highly simplified modelling such as mean field electrodynamics and thin flux tube models have provided significant intuition about large-scale dynamos, but with the advent of modern computing, many of the simple ideas generated have failed to operate in fully nonlinear modelling. Many of these ideas are based upon an essentially kinematic paradigm, where the velocity field is dynamically unaffected by the presence of the magnetic field. We therefore here examine a different scenario, where the magnetic field is dynamic and indeed drives a component of the very flows that then achieve dynamo action, making the induction process now essentially nonlinear. The hope is that such novel dynamo mechanisms might be more robust at high magnetic Reynolds numbers. We illustrate these ideas with a fully nonlinear simulation, and attempt to distill the essence of these results into a simpler semi-analytical mathematical model.