On the modified Taylor constraint

A dynamo driven by motions unaffected by viscous forces is termed magnetostrophic. Although such a model might describe magnetic field generation in Earth’s core well, a magnetostrophic dynamo has not yet been found even though Taylor Proc. R. Soc. Lond. A 1963, 274, 274–283] devised an apparently viable method of finding one. His method for determining the fluid velocity from the magnetic field and the energy source involved only the evaluation of integrals along lines parallel to the Earth’s axis of rotation and the solution of a second-order ordinary differential equation. It is demonstrated below that an approximate solution of this equation for a broad family of magnetic fields is immediate. Furthermore inertia, which was neglected in Taylor’s theory, is restored here, so that the modified theory includes torsional waves, whose existence in the Earth’s core has been inferred from observations of the length of day. Their theory is reconsidered.