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Co-ordinates of heaven and Earth
Published in Martin Vermeer, Antti Rasila, Map of the World, 2019
Together, all these quantities go by the name of Earth Orientation Parameters (EOP). Their changes over time are continuously monitored, and measured values published, by the International Earth Rotation and Reference Systems Service (IERS) on the Internet. The geophysical causes of the temporal changes in these parameters are well understood and can be modelled; one of the main causes of the Chandler wobble are the changes in pressure in the world's oceans and atmosphere (Gross, 2000).
The Earth's rotational modes revisited
Published in Geophysical & Astrophysical Fluid Dynamics, 2023
The Earth's known free wobble/nutation modes are the tilt-over mode (TOM), the Chandler wobble (CW), the free-core nutation (FCN), ICW and the FICN. The periods of these modes are predicted by applying the conservation laws, which are in the form of partial differential equations, to the rotating and deformable Earth. The presence of a large LC bounded by the MT and the IC complicates dealing with these equations. The second-order partial differential equation describing the dynamics of a uniformly rotating, homogeneous and incompressible liquid spherical shell with rigid boundaries is hyperbolic. Hyperbolic equations normally describe initial value problems while in the LC the equation is subjected to boundary conditions, a condition which makes the problem ill-posed. In core dynamics where the objective is to compute the long period modes (inertial modes, for example) of a uniformly rotating spherical shell (Rieutord 1995, Rieutord and Valdettaro 1997, Rieutord et al.2001), or deal with elliptical (tidal) instability of the liquid shell (Cébron et al.2012, for example) liquid of small viscosity is considered to avoid the ill-posed nature of the problem. Estimates of the Ekman number in the liquid core range from the order of 10 up to 10 (Lumb and Aldridge 1991). The displacement of a mass element in the liquid core during the wobble is predominantly rigid rotation and involves negligible shear, therefore, viscosity is ignored.
Rotational modes of Poincaré Earth models
Published in Geophysical & Astrophysical Fluid Dynamics, 2021
In this work we first used a particular solution of the Poincaré equation (3) and the conservation of the Earth's angular momentum (43) to solve for the frequencies of the Spin-over Mode (SOM), Tilt-over Mode (TOM), Chandler Wobble (CW) and Free Core Nutation (FCN) of a simple Earth model. These modes have, of course, been known at least since the time of Bryan (1889) and Hough (1895). Although sections 2 and 3 may be considered a review of the SOM, FCN, TOM and CW, our method is original in that we made use of the reduced pressure χ, which is a scalar variable, instead of the displacement field as it is customary. The advantage of using the scalar field is that after expanding the dynamical equations (3) and (8), only even-degree spherical harmonics are present in the resulting equation (9). This will prove significant for more realistic Earth models when series solutions of the dynamical equations are introduced.