In this simulation we began with a weak magnetic field in the y direction, and forced a shear flow in the x direction (u ~ cosine 2 pi y), that was confined to a narrow layer in the vertical z direction. This would cause the magnetic field to be stretched out into two magnetic structures one with positive field Bx > 0 and one with negative field Bx < 0. We found that if magnetic diffusion was strong (low magnetic Reynolds number) then these two structures would find an equilibrium state within the layer (MPG Movie of magnetic pressure B2). However if we tried a less diffusive simulation then this equilibrium would become unstable and these structures would alternately rise (MPG Movie). If we pushed the magnetic diffusivity even lower, then this rising process became much more irregular (MPG Movie). We also discovered that if we decreased the viscosity in these simulations (increasing the Reynolds number) then the action of buoyant rising would occasionally trigger a Kelvin-Helmholtz instability which would briefly twist a magnetic structure into a helical shape (MPG Movie). (Brummell, Cline, & Cattaneo 2002, MNRAS, 329, L73; Cline, Brummell, & Cattaneo 2003, ApJ, 588, 630)
It is believed that the sun is able to maintain its magnetic fields because of a combination of magnetic field shear stretching (the omega effect) and magnetic field twisting (the alpha effect), which together drive the 11-year sunspot cycle. When we saw these twisting events in our shear simulations, we wondered if these might allow our simulations to maintain a field in a stretch-twist dynamo process. So we tried a new set of simulations: We set the weak initial field so that it was positive in the top half of the domain, and negative in the bottom half. In this way, if there was no dynamo activity, all magnetic fields would diffuse away over time. We also changed the shear so that rather than than having a cosine y profile, instead it was more of a sawtooth function of y, so that it would create one strong magnetic structure in the center (with Bx < 0), surrounded by a weaker magnetic field (with Bx > 0). We found that if magnetic forces were weak, then they were insufficient to create enough buoyant activity to trigger a Kelvin-Helmholtz twisting event, and the system would fail to act as a dynamo, with all magnetic fields slowly diffusing away (MPG Movie of magnetic field Bx, with blue = negative, green=positive). However if magnetic forces were strong enough then they would create a strong buoyant flow, triggering a series of intermittent Kelvin-Helmholtz twisting events, thus causing the system to act as a dynamo. In this dynamo process, the system would produce a series of buoyant magnetic structures of a given polarity (say Bx > 0) which would each rise and twist maintaining the magnetic fields. At irregular intervals, the polarity of the system would reverse and it would then make a series of magnetic structures with the opposite polarity (MPG Movie). This was particularly exciting because the magnetic fields in our sun also reverse polarity at the end of each 11-year sunspot cycle. (Cline, Brummell, & Cattaneo 2003, ApJ, in press)
We put a magnetic flux tube into a background where a convective layer lies on top of a stable layer, in the same way that the sun's convective zone sits above its stable radiative zone. We found that if the magnetic tube was weak, then it would be torn apart by the convection with the remains being pumped down below the convecting layer into the stable zone (MPG Movie of magnetic pressure B2). If the tube is stronger, so that it has a magnetic energy density equal to the kinetic energy density of the convection, then it will almost survive before being shredded (MPG Movie). The only way to hold a tube together is if we make its magnetic energy density larger than the maximum kinetic energy density contained anywhere within the convection. In this case the tube rises successfully until it reaches the upper boundary of our domain, where it slowly diffuses, decreasing in strength until it is weak enough that it can be pulled down into the convection (MPG Movie).
Great web pages that talk about the sun and the solar dynamo problem: