The Zonal Tidal Effect on the Variation in the Rotation Rate of the Earth with a Fluid Core Ñ. Improvements on the Theoretical Formulae

The tidal variation in EarthÄs rotation rate is a periodical response to solarlunar tide generat ing potential (TGP), which can be expressed as a function of the non-dimensional parameter k/cm (k and cm are effective crus-t mantle Love number and effect ive polar moment of inert ia, respectively). When Earth is treated as the one with a elast ic mantle, the equilibrium ocean tide and non-coupling core-mantle, the parameter k/cm can be expressed. The disturbance of nonequilibrium ocean t ide, however, makes k/cm be a complex number and related with its wave frequency. Therefore the tidal series in the variation of EarthÄs rotation rate (VERR) were redefined in IERS (1992) and the more complete tidal series including diurnal and semidiurnal zonal tied were given in IERS (1996) with the deeper research in the high frequency variation of the EarthÄs rotational movement. In this article, the factor of the fluid core, which is related with the variation in the polar moment of inertia of the Earth, is considered and introduced dist inctly into the theoretical formula of the variation in the EarthÄs rotational rate caused by lunarsolar t ide-producing force based on the dynamics principle of the fluid core Earth. Different from previously work, some Doodson developments are given including the variation formulae of the EarthÄs rotational rate, LOD and UT1. The reasons are pointed why the moment of inertia for the scale should be the effective polar rotational moment of inertia of the mantle and the Love number should be the effective Love number of the mantle. It is also indicated that the factor of the fluid core is consistent with the effect of the effective Love number of the mantle due to fluid core.