On the possibility of quantifying diffusion and horizontal Lorentz forces at the Earth’s core surface

If the main magnetic field at the core surface changes in time only as a result of its advection by fluid motions (i.e. under the frozen-flux (FF) assumption), it should satisfy a number of integral constraints. Additional similar constraints should apply if the flow is further assumed to be tangentially geostrophic or purely toroidal. Those integral constraints have been used in the past to test each of these assumptions. Possible violation of some of the frozen-flux constraints have led to the suggestion that significant diffusion could have occurred below South Africa in the past century. This suggests that diffusion could indeed be quantified with the help of those integrals. Here, we consider this possibility in general terms, and show that when all assumptions are relaxed, the no-longer zero values taken by those integrals could be used, at least in principle, to infer some quantitative information about the amount of diffusion and horizontal Lorentz forces acting everywhere at the core surface. The extent to which those theoretical results could be of any practical use remains to be assessed.