Rotation of a deformable earth with dynamical superficial fluid layer and liquid core. I - Fundamental equations

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Earth Rotation, Euler Equations Of Motion, Geophysical Fluids, Mathematical Models, Rotating Fluids, Angular Momentum, Hydrodynamics, Love Waves

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The paper presents a theoretical development leading to the governing equations for the rotation of a three-layer precessing earth. A Love number approach is used to describe the inertia tensor's changes due to the elastic deformation under the influence of the various acting potentials. The liquid core and the superficial fluid layer are seats of 'simple motions' of Poincare (1910). The use of the angular momentum law in each part yields a nine-equation system, of which the unknowns are the components of the instantaneous rotation vectors of the different layers. A numerical estimation of the various terms appearing in equations leads to a possibility of calculating two types of solutions. On the one hand, the variations of the axial rotation of the mantle, of the core and of the superficial layer are derived. On the other hand, the free frequencies of the coupled tesseral system are presented. In the last section, more complete equations for the rotation of a three-layer earth are proposed.

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