Compressibility,core dynamics and the subseismic wave equation

It is shown that in the dynamics of a deep fluid of planetary scale such as the Earth's core, compressibility, stratification and self-gravitation are all important as well as rotation. The existing proof of Cowling's theorem prohibiting non-stationary axisymmetric dynamos, and the application of the Proudman-Taylor theorem to core flows, both based on the assumption of solenoidal flow, need to be reconsidered. For sufficiently small (subacoustic) frequencies or reciprocal time scales, an approximation which neglects the effect of flow pressure on the density is valid. We call this the “subseismic approximation” and show that it leads to a new second-order partial differential equation in a single scalar variable describing the low frequency dynamical behaviour. The new “subseismic wave equation” allows a direct connection to be made between the various possible physical regimes of core structure and its dynamics.