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On the effects of an imposed magnetic field on the elliptical instability in rotating spheroids

The effects of an imposed magnetic field on the development of the elliptical instability in a rotating spheroid filled with a conducting fluid are considered. Theoretical and experimental studies of the spin-over mode, as well as a more general short-wavelength Lagrangian approach, demonstrate that the linear growth rate of the instability and the square amplitude of the induced magnetic field fall down linearly with the square of the imposed magnetic field. Application of the results to the Galilean moon Io confirms the fundamental role played by the elliptical instability at the planetary scale.