Hydromagnetic waves in a rotating sphere

Abstract

The Earths’outer core is modelled by the interior of a rotating sphere containing an incompressible, inviscid, perfectly conducting fluid of constant density. Solutions are sought as small perturbations to the governing equations in the cylindrical coordinates (r, θ, z), linearized about a state of no flow and azimuthal magnetic field varying with r. A multiple scale perturbation technique is used to approximate slow hydromagnetic waves. This scheme assumes short wavelength scales (i.e. much less than the radius of the sphere) in the r and θ directions while the wave number in the r direction varies slowly (on the scale of the spherical radius) with r. The length scale in the z direction is long and the amplitude varies on the long length scale in both r and z. The waves are also assumed to be in geostrophic balance. The approximation is found to be generally valid only in a region bounded away from the equator. It becomes singular in the neighborhood of the equator, and this singularity does not, in general, appear to be removable. The waves are found to propagate both east and west, and may exhibit trapping. The possible relation of these results to the westward drift of the Earth's magnetic field is discussed.

Key words:

• Earth's core
• MHD waves
• rotating fluids