On Ohmic heating in the Earth's core I: nutation constraints

We present calculations to place formal lower bounds on the energy dissipated by the magnetic field in the core. These bounds are discovered by solving for 3-D magnetic fields in the Earth's core that are optimally configured for minimizing the dissipation. Such bounds are relevant for addressing the balance of heat flow through the core-mantle boundary into the mantle, and thus for constraining Earth's history scenarios. The bounds we derive are based on a number of different constraints. We use observed values of the magnetic field at the core-mantle boundary for epoch 2001, and also the root-mean-square values of the radial magnetic field on the inner core boundary and the core mantle boundary inferred from interpretations of the Earth's nutations. A formal lower bound for the dissipation based on all the constraints is almost 10 GW. This lower bound is achieved for a 3-D magnetic field configuration that has very unlikely features. We present two further geophysically reasonable (but no longer rigorous) calculations that raise the dissipation towards 100 GW, not dissimilar to other recent estimates of dissipation.