We present the results of numerical simulations of normal modes of the mean flow due to the superposition of cyclonic and anticyclonic vortices at high latitudes. Such a flow structure is often observed in the upper troposphere — the lower stratosphere in winter. Our aim is to identify normal modes in the oscillation spectrum that resemble torsional oscillations. We solve the problem numerically, using a barotropic quasi-geostrophic model. Additionally, we estimate the dependence of the normal modes on experimental parameters (the number of spherical harmonics in the stream function field expansion, the parameterization of viscosity and hyperviscosity). The simulation results show that flow instability almost always increases with increasing amplitude of the anticyclonic vortex to varying degrees at different viscosities and different numbers of harmonics in the field expansion. The spatial structure of the most unstable normal modes changes most chaotically when the experiment parameters and the mean flow change. This significantly complicates the interpretation of real oscillations in terms of normal modes, including the interpretation of torsional oscillations. Axisymmetric normal modes are often present in the spectrum, but they do not have all the properties of torsional oscillations and do not dominate the spectrum.