I’d like to take you on a journey to the outer core: home to an important process which scientists refer to as the Geodynamo. This process is responsible for the generation of magnetic fields in the liquid iron and nickel layer between the inner core and lower mantle.
The exact mechanisms that occur to bring about this dynamo are not well known, for obvious reasons: inaccessibility to earth’s deep interior, and the complexity and chaotic behavior of magnetic field measurements. But the main idea that it was in fact the liquid metal, not the solid iron of the inner core, that generated the magnetic field, gave rise to an important equation we refer to as the Induction Equation.
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| A snapshot of the simulated geomagnetic field produced by Glatzmaier and Roberts (1995). The lines follow the paths of magnetic fields generated from fluid motions. |
This equation was brought on by scientific discoveries in the 40s and 50s, which were mainly motivated by the studies of magnetized plasma and conductive fluids. Using the building blocks of Maxwell’s equations for electric and magnetic fields, and combining this with the Navier-Stokes equation for a fluid, we arrive at the induction equation:
The analogy to the dynamics of a fluid is rather profound here. The first term is a common diffusion term, showing that energy is lost by the electrical resistance of the material, as a form of heat dissipating through friction. The second term is analogous to vortex stretching: imagine you are holding a string vertically on both ends, and in the middle a ball is attached. As you swing the ball around, you sweep a circle roughly parallel with the ground. But pull the two ends together and the ball gets faster. The general idea is reflected as vortices, or swirls in the fluid, naturally elongate, or stretch, as a property of turbulence. To not overcomplicate things, the general idea is that as these vortices stretch the preexisting magnetic field, thereby strengthening it.
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To carry this important term back to the dynamics of the outer core, one can see that essentially that what the existing velocity field is has immense implications for whether or not the total magnetic field will grow or decay. Without a velocity field that can stretch the magnetic fields, the magnetic field will naturally decay.
This equation is inherently complex and nonlinear, and so solving it analytically is difficult. Computational simulations use advanced numerical methods and algorithms that break down the equation into manageable steps and approximate the solutions over small time intervals. Over the past 20 years, simulations based on the induction equation have been successful in replicating a dynamo, but it is still unclear as to what the exact dynamics are, specifically on earth, that have allowed this magnetic amplification.
References
1. R. Beck, Magnetic fields in spiral galaxies, The Astronomy and Astrophysics Review, 24, 4 (2015)
2. Bondi, Hermann Sir and Thomas Gold. “On the Generation of Magnetism by Fluid Motion.” Monthly Notices of the Royal Astronomical Society 110 (1950): 607-611.
3. Glatzmaiers, G., Roberts, P. A three-dimensional self-consistent computer simulation of a geomagnetic field reversal. Nature 377, 203–209 (1995). https://doi.org/10.1038/377203a0
Elaine, for this exercise you should aim to speak to the most general audience about the importance of Earth's magnetic field (especially to animals living on the planet's surface) and attempts to recreate it in the laboratory. I might start off talking about how the magnetic field protects us from harmful solar radiation in space, and then dive nearly 1500 miles down into Earth's outer core where swirling liquid metal driven by the spinning planet creates the magnetic field. You might also mention that the solid inner core (over 3000 miles down) is so hot (nearly the Sun's surface temperature) that it cannot be the cause of the magnetism. Then you can dive into the laboratory where you describe a 3 meter sphere (might use English units) filled with highly reactive liquid sodium is being spun at high speeds (how fast to simulate the spinning of the planet?) to try to initiate the liquid dynamo. This might be as far as you can get in the initial blog, but you will want to find illustrations that show a cross section of the planet with a superimposed magnetic field and of the 3 meter sphere (maybe with you as scale). The equation exercise will come later.
ReplyDeleteHi Elaine, I enjoyed your post. I thought it was very interesting and informative (although maybe a little too scientific for a general audience). You mentioned how the magnetic field protects us from solar radiation, and I think that would be a great point to add in the introduction. The demonstration that you did in class was really cool, and I think that adding a picture of a tornado might help support that idea when considering your third figure. Nice work!
ReplyDeleteP.S. 3000km is slightly less than 1900 miles, if you wanted to add some context for American readers.
Hi Elaine, I really liked your blog post! I found it very informative and fascinating. The image of the simulated magnetic field was very helpful in demonstrating the complexity of Earth's magnetic field. I agree with what was discussed in class as some of the terminology is a bit too advanced for the general audience. I thought your demonstration in class was very helpful and if you included that in your post it would help the general audience grasp the concept of vortex stretching. Nice job!
ReplyDeleteHey Elaine! I think it would be easier to make your blog more accessible if you changed the content! Similar to the suggestions made by Dr. Kaufman, telling the audience about what the geodynamo/magnetic fields are, talking about why its important (solar radiation) and briefly on how scientists (including you!) are studying it would work swell. I would honestly cut out the entire induction equation part (since you could use it for a later blog). Otherwise, awesome job and I loved the demonstration during your talk!
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