A Hamiltonian approach to dissipative phenomena between the Earth's mantle and core, and effects on free nutations

The Hamiltonian formalism was recently applied by Getino (1995a,b) for the study of the rotation of a non-rigid earth with a heterogeneous and stratified liquid core. That earth model is generalized here by including the effect of the dissipation arising from the mantle-core interaction, using a model similar to that of Sasao, Okubo & Saito (1980), which includes both viscous and electromagnetic coupling. First, a solution for the free nutations is obtained following a classical approach, which in our opinion is more familiar to most of the readers than the Hamiltonian treatment. This solution provides a theoretical basis clear enough to study both the qualitative and quantitative effects of the dissipations considered in the hypotheses. The main qualitative features are, besides the delays, that the free core nutation (FCN) suffers an exponential damping, while the chandler wobble (CW) is not damped at first order, by the dissipation considered. The numerical values obtained for the complex compliances agree with the most recent experimental computations.
Next, the problem is studied under a Hamiltonian formalism, and a solution equivalent to the above is obtained. Besides its interest from a theoretical point of view, this formalism is necessary in order to apply canonical perturbation methods in order to obtain analytical nutation series.     

Magnetostatic and electrostatic torques within a planet

Several dynamic agencies control differential rotation between various regions of a rotating gravitating body such as a planet, namely advection of angular momentum (within fluid regions) and torques due not only to (a) viscous forces, (b) dynamic pressure forces and (c) gravitational forces, but also to (d) Lorentz forces (involving the flow of electric currents in electrically conducting regions), (e) magnetostatic forces (when magnetized material is present) and (f) electrostatic forces (due to the presence of electric charges). Torques due to (a), (b), (c) and (d) have already been treated in the literature, some extensively. It is of general theoretical interest to derive from first principles mathematical expressions for torques due to (e) and (f), even though they turn out to be quantitatively insignificant in the case of the Earth.     

Oceanic excitation of daily to seasonal signals in Earth rotation: results from a constant-density numerical model

Velocity and mass fields from a constant-density, near-global ocean model, driven with observed twice-daily surface wind stresses and atmospheric pressures for the period October 1992-September 1993, are used to calculate oceanic excitation functions for the length of day (LOD) and for polar motion (PM), and results are analysed as a function of the frequency band. Variable currents and mass redistributions are both important in determining oceanic excitation functions. For bands with periods longer than one month, wind-driven variability is the primary cause of oceanic excitation signals. At higher frequency bands, larger deviations from the inverted barometer response occur, and pressure-driven signals contribute more significantly to the variance in the excitation functions. Oceanic LOD excitation is generally small compared to that of the atmosphere, except for the 2-10 day band. At these scales, adding oceanic to atmospheric excitation series does not lead to better agreement with the observed LOD, although this result may be related to data quality issues. With regard to the excitation of PM, the ocean is in general as important as the atmosphere at most time scales. Combined oceanic and atmospheric excitation series compare visibly better with geodetic series than do atmospheric series alone, pointing to the ocean as a source of measurable signals in PM.