Tidal variations of Earth rotation

TLDR

The study focuses on periodic variations in Earth’s rotation caused by tidal deformation from the Sun and Moon, applying to the coupled mantle, crust, and oceans, and examines how the parameter k/C—where k reflects the Love number contribution to the moment of inertia and C is the polar moment of inertia—varies with core–mantle decoupling and ocean loading. The authors rederived the rotational tidal series, retaining all terms with amplitudes ≥0.002 ms, and theoretically estimated the effects of ocean tides on Earth rotation, nutation, and polar motion using Laplace tidal equation–based models. They found that ocean tides increase k by 0.04, and lunar laser ranging data show k/C at monthly and fortnightly frequencies to be 0.99 ± 0.15 and 0.99 ± 0.20, respectively, close to the theoretical value of 0.94 ± 0.04.

Abstract

We have rederived the periodic variations of the earth's rotation due to the tidal deformation of the earth by the sun and moon and included all terms with amplitudes ≥0.002 milliseconds (1 mm). This series applies to the mantle (plus crust) and oceans, which rotate together for characteristic tidal periods. The parameter which scales the rotational series is k/C , where k is that fraction of the Love number which causes the tidal variation in the moment of inertia of the coupled mantle and oceans while C is the dimensionless polar moment of inertia of the coupled units. If the whole earth (minus oceans) were coupled rotationally, then k = 0.30 and C = 0.33. Ocean tides increase k by 0.04. Decoupling of the fluid core from the mantle decreases k by 0.06 while C = C mantle = 0.29, since neither pressure, viscous, nor hydromagnetic coupling locks the fluid to the mantle for periods less than 5 to 25 years. From the analysis of lunar laser ranging data we find that k/C at monthly and fortnightly frequencies equals 0.99 ±0.15 and 0.99 ± 0.20 as compared with a theoretical value of 0.94 ± 0.04. In addition, we have estimated theoretically the effects of ocean tides on earth rotation, nutation and polar motion using models based on the Laplace tidal equations.