Taylor's Condition

Taylor's condition

Taylor's condition, first derived by J.B. Taylor in 1963, is a statement about the electromagnetic torque within the Earth's core, namely that it must vanish when integrated over cylindrical shells parallel to the axis of rotation. It is one of the most important results in geodynamo theory.

Basic equations

The two equations we will need are the induction equation:

governing the evolution of the magnetic field B in the core, and the Navier‐Stokes equation (in its simplest, Boussinesq form):

governing the fluid flow U. In general there would also be an equation for the thermal and/or compositional buoyancy that ultimately drives the whole system, but for our discussion here we can take the buoyancy force F _T to be prescribed. The only feature that will matter is that it is purely radial.

In these equations, length has been scaled by r ₀, time by , U by , and B by , where r ₀ is the outer core radius, the magnetic diffusivity, the Earth's rotation rate, the density,...