@article {2968,
	title = {Dynamics of the Earth{\textquoteright}s fluid core: Implementation of a Clairaut coordinate system},
	journal = {Physics of the Earth and Planetary Interiors},
	volume = {227},
	year = {2014},
	pages = {61 - 67},
	abstract = {If the reference state of a rotating and self gravitating fluid body is one of hydrostatic equilibrium then\&nbsp;the figure of the body is a spheroid such that a cross sectional area parallel to the equatorial plane of\&nbsp;the body is a circle while that parallel to a meridional plane is an ellipse. The effects of the fluid body{\textquoteright}s\&nbsp;flattened (spheroidal) figure is small on the frequencies of the body{\textquoteright}s short-period (shorter than a few hours in the case of the Earth) normal modes. For the long-period normal modes, however, these effects\&nbsp;must be considered. Furthermore, the body{\textquoteright}s wobble and nutation modes owe their existence to its ellipsoidal\&nbsp;figure. In the conventional approach to computing these frequencies, an orthogonal coordinate system\&nbsp;is usually considered. It is then necessary to have the knowledge of the derivatives of the material\&nbsp;properties of the body, such as the density and Lam{\'e} parameters, in order to include the effects of the\&nbsp;ellipticity in the dynamical equations. In the available Earth models, however, these derivatives are\&nbsp;not well defined. In order to minimize the effects of these derivatives in the treatment of the dynamical\&nbsp;problems we use a non-orthogonal (Clairaut) coordinate system. Using this approach, we compute the\&nbsp;frequencies and displacement eigenfunctions for some of the inertial modes of a realistic spheroidal\&nbsp;model of the Earth{\textquoteright}s fluid core and compare them to the known results for an Earth model with a homogeneous\&nbsp;and incompressible fluid core.},
	author = {Behnam Seyed-Mahmoud and Ali Moradi}
}
