Part of me kind of wishes that this had some trivial, totally safe and innocuous consequence that you could still appreciate somehow with a Mr. Wizard type experiment.
No, it's a chaotic system that is quasistable for an average of 11 years at a time before it flips to the opposite orientation with respect to the spin axis. The Earth's magnetic field, generated by currents in the liquid outer core, is a similar magnetohydrodynamic system that has no apparent periodicity.
Disclaimer: I worked on the solar magnetic field for two summers.
Whether the sun is chaotic in the technical sense (i.e. the butterfly effect) is still open to question [1]. The solar magnetic field is poorly understood. In the 1980s, everybody thought that a particular model (mean-field dynamos IIRC) had it all figured out, but new observations from helioseismology showed them wrong. Wikipedia has a good article on the solar cycle: https://en.wikipedia.org/wiki/Solar_cycle My advisor wrote a more technical overview: http://solarphysics.livingreviews.org/Articles/lrsp-2010-3/a...
The last time a geomagnetic reversal occurred on Earth was 780,000 years ago (with a possibility of a brief one occurring 41,000 years ago) [1]. I wonder what it will feel like when it happens again...
