A colleague reports a numerical model of the core in which the magnetic field remains…
PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history · The solid Earth: structure, fields and thermal history
The Solid Earth, Ch The geomagnetic field: potential, spectrum, induction and the palaeomagnetic record
Problem
A colleague reports a numerical model of the core in which the magnetic field remains exactly axisymmetric (no dependence on longitude at all) and shows no measurable decay after 2×105yr of simulated time, well beyond the diffusion time τd≈49kyr expected for the core. The colleague argues this is unsurprising: the flow driving the model is itself purely axisymmetric (differential rotation only, no convective cells), and an axisymmetric cause should produce an axisymmetric, steady effect, so there is no contradiction with dynamo theory.
((a)) Is the colleague's reasoning correct? State precisely what Cowling's theorem forbids, and whether it is the flow or the field whose symmetry it constrains.
((b)) Given the theorem, what must actually be true of either the reported field or the reported flow if the model's claim (survival for 2×105yr, no decay) is to be trusted?