On the Origin of the Bi-Decadal and the Semi-Secular Oscillations in the Length of the Day

Abstract

It is presently believed that the liquid core motions that lead to variations in the geomagnetic field and in the Earth’s rotation rate in scales at and above the bi-decadal originate internally. Although, the length of the day (LOD) variations bears some relationship with solar activity and, therefore, either solar activity is exciting some modes of oscillations in the Earth, or these modes have the same external origin in the two bodies. We have introduced a suitable wavelet base function that allows for splitting the modulation in the Hale solar cycle in the Gleissberg cycle and two quasi-harmonic oscillations. They have periodicities in the lower Gleissberg band, 40–60 years and in the Hale, 20–30 years, bands and are baptized semi-secular (SS), and bi-decadal (BD) oscillations, respectively. Here we find that these two modes of oscillations are also visible in LOD variations. But while the bi-decadal modes in sunspot number (R) and in LOD are synchronic and follow each other linearly, the SS modes are non-linearly related, with a time lag in LOD, of 94 years. We compare the SS mode of oscillations in LOD with oscillations in the angular velocity of precession of the solar orbit in the inertial reference frame (Daxym). The lengths of Daxym and LOD SS oscillations vary slightly with their amplitudes, but the relationship between them is always exactly 3/4. The 178.7 year cycle in the modulations of Daxym oscillations is also followed by the SS oscillation in LOD. The wavelet components that correspond to the semi-secular oscillation are in the upper band of the modes of torsional oscillations in the liquid core as inferred from geomagnetic variations. The large time lag of LOD semi-secular oscillation with respect to the exciting force indicates that the torsional oscillations originate deep inside the core. This is consistent with the fact that torsional oscillations have been found to originate near the surface of a cylinder that is tangent to the equator of the inner core. In view to the above findings we discuss a mechanism by which torsional oscillations in the liquid core might be externally excited but internally powered.