I Finally Got the Ocean Into the Solver

My electromagnetic induction solver has officially moved beyond a 1D Earth.

Phase 1 was the starting point.. give the Earth a magnetic field that changes with time, then calculate the currents and heating it induces inside a radially layered Earth.

Phase 2 adds the ocean.

I’m treating the ocean as a really thin conductive shell wrapped around the planet. Conductivity changes from place to place, so the same changing magnetic field can drive different currents in different parts of the ocean.

Those ocean currents create their own magnetic field. That field interacts with the conducting Earth below, and the Earth responds, too. That response then changes the electric field driving the ocean currents.

So, everything feeds back on everything else a little. The solver has to keep going until the pieces agree.

The bridge between the ocean and the 1D Earth comes from the Sun-Egbert [1] thin-sheet formulation.

Basically, Sun & Egbert give us a way to take the Earth’s radial electromagnetic response and connect it to the conductive ocean using two mathematical response modes, poloidal and toroidal. Those get built into a Green operator that tells the model how currents in one part of the ocean affect electric fields somewhere else.

For the real SWARM forcing I’m testing here, I get about56.0% of the dissipated power in the ocean and 44.0% in the solid Earth.

That’s with real geographic ocean conductance and a realistic five layer Earth conductivity model.

So, now I can calculate how electromagnetic energy partitions between the ocean and solid Earth. What Phase 2 still can’t tell me is where in the water column that ocean heating happens.

That’s Phase 3.

And it gets me closer to the question I actually built this thing to answer: When electromagnetic energy enters the Earth system, where does it go?

References

[1] Sun, J., & Egbert, G. D. (2012). A thin-sheet model for global electromagnetic induction. Geophysical Journal International, 189(1), 343–356. https://doi.org/10.1111/j.1365-246X.2012.05383.x