On asymptotics of low-frequency oscillations of the liquid core: 2. Frequency dependence of the inertial core-mantle coupling

New, unique information on the inertial and dissipative coupling of the liquid core and the mantle has been retrieved from modern high-precision (radiointerferometer and GPS) data on tidal variations in the rotation velocity and nutation of the Earth. Comparison of theoretical and observed data provided new estimates for the dynamic flattening of the outer liquid and the inner solid cores, mantle quality factor, viscosity of the liquid core, and electromagnetic coupling of the liquid core and the mantle [Molodensky, 2004, 2006]. As was shown in the first part of the paper [Molodensky, 2008] (further referred to as [I]), generation of eddy flows in Proudman-Taylor columns, whose orientation is controlled by the topography of the liquid core-mantle boundary, should be taken into account for correct estimation of the inertial coupling (see formulas (8) and (34) in [I]). The range of periods within which this effect plays a significant role is determined by the decay time of these flows. This time is estimated in the paper for the case where dissipation is related to viscous friction at the core-mantle boundary or with the electromagnetic coupling of the liquid core and the mantle. Because of significant uncertainties in modern data on the viscosity of the liquid core, the magnetic field intensity at the core-mantle boundary, and the electrical conductivity of the lower mantle, the dissipative coupling of the liquid core and the mantle cannot be calculated as yet. However, as shown in the paper, the decay time of eddy flows is connected with the attenuation time of subdiurnal free nutation and with the liquid core viscosity. This enables the estimation of the frequency dependence of the dissipative coupling in a fairly wide range. It is shown that the range of periods for which relations (8) and (34) in [I] are valid encompasses the best-studied length-of-day variations and, therefore, these relations are applicable to analysis of the majority of modern data.