Hydrodynamic instabilities in the tachocline resulting from layer thickness variations

The paper presents results of numerical experiments with the quasi-geostrophic model in the shallow water approximation. The model has been used to estimate hydrodynamic instabilities in the solar tachocline, resulting from layer thickness variations. Calculations show that local disturbances of the layer thickness result in destabilisation of differential rotation, even if profile of differential rotation is stable relative to barotropic disturbances. Period of the instability excitation depends largely on the position and depth of thickness inhomogeneities of liquid layer. Penetrative convection cells can be the major cause of disturbances of the tachocline thickness. The same instabilities can appear in the thin upper layer above the convective shell.