Grant: Discovery Grants Program - Individual

The objectives of the proposed research project are: (1) to use numerical techniques to compute, accurate to second-order-terms in the ellipticity of the equipotential surfaces, the frequencies of the Earth's normal modes, especially those of wobble and nutation for which observed frequencies are known; (2) to study the effects of elliptical instability on the viscous coupling between the Earth's fluid core and the inner core and mantle; we also plan to study the role of the elliptical instability on the planetary magneto dynamo; (3) to use experimental techniques to study the wave number one modes of a fluid shell proportional to the Earth's fluid core. These will improve the accuracy of the predicted frequencies of these modes and, therefore, help improve our knowledge of the Earth's deep interior properties. This, in turn, will help better predict the future state and behaviour of our planet. The conventional approach to the normal mode theory suffers from two major shortcomings: (a) it is accurate to first order in the ellipticity of the equipotential surfaces, and (b) the heavy truncation of the coupled chains of ODEs resulting from the expansion of dependent variables in series of spherical harmonics makes it impossible, for almost the entire spectrum, to check the convergence of the results. This is particularly a problem in the fluid outer core where severely truncated series are unlikely to satisfactorily represent the complicated geometry of the eigenfunctions of long-period modes. In order to minimize the effects of these shortcomings we have developed a new approach in which the number of equations is reduced to three and, with the application of a Galerkin method, the order of the ODEs is reduced to one. We have used this approach to compute the periods of some of the long period core modes. We plan to extend our approach to the Earth's nutation modes. This is an important step as in recent years, with the help of very-long-baseline radio interferometers (VLBI), the accuracy of the observed periods of these modes has improved significantly. Therefore, the theory needs also be revised in order to better present the physics of the interior of our planet.