Wave motions in rotating, spherical, hydromagnetic experiments

The geodynamo problem---understanding how Earth's magnetic field arises---has seen great progress in recent years, from self-generation in many numerical simulations to the Bullard-von Karman dynamo achieved in an experiment by Bourgoin et al. (New J Phys 8 12:329, 2006). First, motivated by the geometry of the Earth, we have constructed a 60~cm differentially rotating spherical shell for experiments with liquid sodium, observing the presence of inertial modes at certain rotation rate combinations (Kelley et al., to appear in Geophys Astro Fluid 2007). The experimental inertial modes match analytically-known inertial modes of the full sphere in their wavenumbers, frequencies, and spatial structures. Second, motivated by Dudley and James's observation (Philos Tr R Soc S-A 425 1869:407-429, 1989) of dynamo action in numerical simulations, we have modified the above spherical system to allow S1T1 forcing in a rotating, full sphere. Again wave motions are present, and initial results are consistent with the dispersion relation for full-sphere Rossby waves.