For instance, the ratio of the rotation to viscous timescales, as measured by the Ekman number Ek, is supposed to be extremely small in the EarthвЂ™s core for which Ek = O(10 в€’15). For the same reason, current numerical simulations operate in a parameter regime that is far away from what is thought to be the one in which the geodynamo operates. Numerical geodynamo models (Christensen & Wicht 2015) can capture qualitative features of the geomagnetic secular variation and of the spatial structure of the geomagnetic field at the coreвЂ“mantle boundary (CMB) but the whole temporal spectrum is impossible to cover due to the prohibitive computational costs required. This variability is the observable consequence of the rich dynamics taking place in the EarthвЂ™s outer core, where the geomagnetic field is generated and continuously altered by the complex interplay between fluid flows and the geomagnetic field itself (Jackson & Finlay 2015 Roberts 2015). The EarthвЂ™s magnetic field shows oscillations and variations on a wide range of temporal scales (Hulot etВ al. Implementation of magnetic diffusion is also briefly considered.Д¬ore, Rapid time variations, Numerical modelling 1 INTRODUCTION The excellent agreement we found with the analytical solution proves that numerical integration of the QG system is possible and that it preserves important physical properties of the magnetic field. We derive a novel analytical solution describing the evolution of the magnetic field under these assumptions in the presence of a purely azimuthal flow and an alternative formulation that allows us to numerically solve the evolution equations with a finite element method. Here we carefully analyse the properties of the resulting equations and we validate them neglecting the action of the Lorentz force in the momentum equation. but the projection of the governing equations on the equatorial disc is handled via vertical integration and mass conservation is applied to the velocity field. The diffusion-free, QG system derived here is similar to the one derived in Canet etВ al.

Over these timescales, rotation is assumed to be the dominant force and fluid motions are strongly invariant along the direction parallel to the rotation axis.

We derive a quasi-geostrophic (QG) system of equations suitable for the description of the EarthвЂ™s core dynamics on interannual to decadal timescales.

Comsol 5.3 negligence inertia