Abstract <p>The Boussinesq approximation generalized with respect to compressibility of the liquid core is used in direct numerical 3D simulation of turbulent thermal convection in a spherical shell. The simulation employed Archimedes, Rossby, Reynolds and Péclet numbers corresponding to <i>Ar</i> = 10¹⁰, <i>Ro</i> = 10⁻⁷, and <i>Re</i>&#xa0;= <i>Pe</i> = 10⁶. Introducing into the model Reynolds and Péclet numbers, which were taken equal to 1 in the earlier simulations, has allowed the increase in Rayleigh number up to <i>Ra</i> = 10²², taking their large values into account. Modeling results indicate the formation of horizontal structures orthogonal to the axis of rotation in the liquid core, which move in opposite directions in the rotating spherical shell. Averaged rotation velocity of the core is characterized by turbulent oscillations similar to the observed length of day oscillations (LOD).</p>