The magnetic field of the sun should have disappeared a long, long time ago. But it's still there, flipping every 11 years. The Solar Tachocline is a thin layer inside the sun which begins at about 0.7 of the sun's radius and ends at about 0.75 of the sun's radius. There is a lot shearing in this layer, ideal for twisting of magnetic lines. A set of equations has been derived to model this layer. There is at least 1 instability in these equations, and which instability is observed depends on the values of a set of parameters.
But what is interesting about these instabilities is the following:
1. when one of these instabilities occurs a lot of magnetic energy is generated but only for a small number of values for the aforementioned parameter set;
2. if you run a simulation for long enough (1 month on 64 HPC CPU cores) 2 large vortices are also created, one in each hemisphere but not at exactly the same time. They both initially travel westward, but then they both stop but at slightly different times. They then both accelerate eastward but not together, then stop accelerating but continue to travel eastward, catching each other up and overtaking each other as if in a race, and when they do overtake each other the vortex doing the catching up is given a slingshot effect by the other and accelerates away but drags the other with it, and the process repeats itself. When they pass each other poloidal magnetic energy is also generated. This continues for a very, very long time until they both travel in parallel, slow down and merge into 1 large vortex whose axis of rotation is normal to the sun's equator. It is my theory that eventually this one merged vortex slows down and stops, unravels and the whole instability occurs again and the two vortices appear and do their thing again. And so on so forth. But this dynamo takes rather a lot of kinetic energy out of the sun, and eventually the sun will stop rotating, Whether this occurs before the sun burns up can be calculated/estimated.
It is also possible that when the initial instability is generated the 2 vortices are not quite generated in full and are only partially created and get stuck in a cycle where they begin to form but there isn't enough energy to quite flip the magnetic lines to create the full vortex so they try again but fail, and try again but fail, and this cycle continues and is still continuing this very second. This also generates magnetic energy for the solar dynamo. It is a theory of mine that this process creates a pumping effect and that there is a range of the parameter set that generates this pump-like process that has a frequency of 1 pump for every sun spot cycle, i.e. this pump creates the sun spot cycle by twisting and both pushing up flux tubes and dragging them back down.
So that's 2 theories for the solar dynamo and 1 for the sun spot cycle.
However, there are some possible assumptions about boundary conditions that could discredit this.
Remember that all this is going on at 0.7 of the sun's radius which we cannot see in the detail we can at the sun's surface.
But these vortices can also explain the sun spot cycle, because the northern vortex rotates anti-clockwise and the southern vortex rotates clockwise! This is what we observe in sun spots. They flow in these directions.
And not only that.
Because we have only been observing sun spots for a few hundred years or so, if these vortices are rotating about an axis that is not quite normal to the sphere, i.e. they are wobbling a bit, or the tachocline is not exactly spherical, and are a source inside the sun to twist the magnetic tubes to generate the sun spots, then it is possible that, because the sun spots currently sort of appear together in the north and south, we are at a point in time when those two vortices are travelling together and have not yet merged into 1 large vortex (in which case we should be able to predict solar behaviour to some degree), and that a long time ago the sun spots would not have appeared together and the northern sun spots would appear several years before the sun spots in the south, the northern sun spots perhaps on the other side of the sun when the southern sun spots would at the same time be appearing on the side facing us. A bit of archeaological research may prove this.
How these vortices actually form is fascinating too, and from my visualisations of them forming you would see what I mean about the pumping effect I've just described.
I have not been able to find a parameter set that can produce this pumping effect for a long time but was close with one set of values (the parameter set is almost infinite). It did it for 3 cycles with the correct times but eventually decayed. SO CLOSE!
But it is my theory that the solar dynamo and sun spot cycle are due to this instability and either:
1. the 2 vortices forming in full, chasing each other for a very long time, until eventually merging into 1 large vortex which unravels for the whole thing to repeat and repeat, etc. until the sun's kinetic energy is used up;
2. or the 2 vortices do not quite form and get stuck in a cycle of trying to form but failing, generating magnetic energy each time they try, and that this has a pumping effect that produces the sun spots and solar cycle and that this pumping has a frequency of 1 pump every 1 solar cycle.
1. generates lots of magnetic energy in one go then lots of smaller amounts of magnetic energy as the vortices pass and overtake each other, but this is repeated over a long time scale, and if the angle of the axes of rotation of these vortices is not normal to the surface this can provide a mechanism to push/pull flux tubes enough to generate sun spots if the angular frequency is correct.
2. continuously generates lots of smaller amounts of magnetic energy with a much larger and constant frequency over the same time scale than 1. but provides a pumping mechanism for pushing/pulling flux tubes.
So 1 large boost in magnetic energy followed by lots of smaller additions to magnetic energy but requires the vortices to wobble.
Or a pumping mechanism to generate frequent but smaller additions of magnetic energy.
In both, the vortices rotate in the direction we observe sun spots to flow.
I'd say option 2. has more going for it. Because I was so close to finding the parameters to simulate the pumping for the frequencies we observe in the solar cycle.
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