Changes in the Earth's rotational velocity and figure deformation associated with them

V.Yu. Belashov^a∗ , E.S. Belashova^b∗∗ , O.A. Kharshiladze^c∗∗∗

^aKazan Federal University, Kazan, 420008 Russia

^bKazan National Research Technical University named after A.N. Tupolev, Kazan, 420111 Russia

^cIvane Javakhishvili Tbilisi State University, Tbilisi, 0179 Georgia

E-mail: ^∗vybelashov@yahoo.com, ^∗∗bel_lena@mail.ru, ^∗∗∗o.kharshiladze@mail.ru

Received July 26, 2019

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DOI: 10.26907/2541-7746.2020.1.66-76

For citation : Belashov V.Yu., Belashova E.S., Kharshiladze O.A. Changes in the Earth’s rotational velocity and figure deformation associated with them. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2020, vol. 162, no. 1, pp. 66–76. doi: 10.26907/2541-7746.2020.1.66-76. (In Russian)

Abstract

It is established that continuous changes of angular velocity of rotation of the plastically-elastic Earth should cause the continuous coupled deformation of a crustal layer, redistribution of masses in a sub-crustal layer and the change of density associated with it, and also, as a consequence of these phenomena, a polar pulsation of a figure when polar diameter of the Earth increases and decreases with time. The mechanism of occurrence of deformations of the planet body under action of a deforming (centrifugal) variable force is found; the tensors of deformations and pressure are written out; and, on the basis of the rheological equations, the equations of balance are deduced, and also calculation of the module of change of polar compression and radial displacements is made at real fluctuations of angular velocity of rotation of the Earth. The calculated values give the quite real changes of compression and radial displacements of the Earth’s crust and its other shells. The opposite process is also shown, namely: the observed fluctuations of amplitude of the polar compression, which lead to respective alterations of the moment of inertia of the Earth, quite correspond to real fluctuations of the day length.

Keywords: Earth’s rotation, fluctuations of angular velocity, figure of Earth, deformation, radial displacements, polar pulsation of figure, equilibrium equations

Acknowledgments. The work is performed according to the Russian Government Program of Competitive Growth of Kazan Federal University and supported by the Shota Rustaveli National Science Foundation (project no. FR17 252).

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