Millennial axially symmetric Magneto-Coriolis modes in Earth's fluid core

Magneto-Coriolis (MC) modes in Earth's fluid core involve oscillations sustained by the combined effect of the Lorentz and Coriolis forces. Here, we investigate the properties of MC modes that involve purely axisymmetric flow, which we term axiMC modes. We provide a basic description of the wave dynamics of these modes, and simple predictions for the expected scalings of their frequency omega, decay rate lambda and quality factor Q based on a uniform ambient magnetic field. In particular, Q scales with the Elsasser number Lambda, which depends on the square of the r.m.s. strength of the azimuthally averaged meridional field. When Lambda>1, Q>1 and axiMC modes may be excited; when Lambda << 1, Q << 1 and axiMC modes revert to quasi-free magnetic decay modes. We present computations of axiMC modes in an inviscid, electrically conducting sphere for two idealized ambient magnetic field configurations, a uniform axial field and an axial poloidal field. We show that a flow gradient in the axial direction is a key property of axiMC modes. For the uniform axial field, omega, lambda and Q follow the scalings expected for a uniform field. For the axial poloidal field, the structure of the modes changes substantially when Lambda greater than or similar to 1, becoming more concentrated in regions of lower field strength. The combination of this structural change and advection of field lines by flow significantly increases lambda, resulting in a Q that remains close to 1 even at high Lambda. For a magnetic field strength inside the Earth's core of a few mT, the gravest axiMC modes are expected to have periods in the range of one thousand to a few thousand years and a Q not substantially above 1. AxiMC modes may be connected to a part of the observed millennial changes in Earth's magnetic field, may exchange axial angular momentum with the mantle, and hence may also explain a part of the observed millennial changes in length of day.