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Quasi-free-decay magnetic modes in planetary cores

A new category of hydromagnetic waves in a rotating conducting fluid within a spherical shell geometry is investigated. These quasi-free-decay magnetic modes are based on particular solutions of the induction equation where the magnetic diffusion plays the central role. These solutions, normally only decaying with time, become propagative owing to the combined action of the background magnetic field and the rotation. The amplitude and sign of their azimuthal phase drift strongly depend on morphology and magnitude of the background magnetic field. The validity domain of these quasi-free-decay (QFD)-modes is related to the Elsasser number and is written as Λ ≪ 1. It follows that these modes dissipate quickly before propagating out. This restriction falls when the above criterion is no longer fulfilled (Λ ∼ 1), the corresponding modes evolving towards distorted QFD-modes. A systematic study of these QFD-modes is made in the limit of small Elsasser number (Λ ≪ 1), for the different symmetries allowed. Application to the Earth's and other planetary cores is then examined for an Elsasser number up to Λ ≈ O(1), in relation to the geomagnetic secular variation and the frozen-flux approximation.