Specific features of development of two-dimensional convection in a rotating compressible conducting fluid

An axisymmetric model of convection in a rotating cylinder in an external uniform magnetic field has been considered. In the considered model, the meridional circulation is created by a nonuniform rotation of the lower boundary relative to the other boundaries. In the considered model, the time of formation of the stationary regime in the magnetic field considerably increases if the vertical density (compressibility) inhomogeneity is taken into account for Ekman numbers of E = E _M = 3 × 10⁻³. This example shows that the compressibility of a medium should be taken into account in the convection and dynamics of the magnetic field when the magnetohydrodynamics of the Earth is analyzed.