Abstract:

A dynamical model is proposed for the elliptical instability that has been reported by Aldridge et al. [Aldridge, K.D., Seyed-Mahmoud, B.,  Henderson, G.A., van Wijngaarden, W., 1997.  Elliptical instability of the Earth’s fluid core. Phys. Earth Planet. Inter., 103, 365–374] in connection with recent experiments on an ellipsoidal shell of rotating fluid. The 
frequencies and growth rates of the instability are obtained numerically  by means of a Galerkin method that is based upon the normal modes of the contained fluid. A finite-element method has been employed to  approximately solve the ill-posed Poincare´ problem for the normal  modes. The numerical results for a special case are compared with their  analytical counterparts, and the agreement is to within 0.1% for shells of small ellipticity. Results are presented for other cases, including some where the boundary perturbation is allowed to rotate slowly with respect to the inertial frame. The conclusion is that such investigations are of  geophysical interest, since tidal forcing might be sufficient to excite an  elliptical instability of the fluid outer core of the Earth and thus contribute to the geomagnetic field.