Vortex-induced vibrations (VIVs) of wind turbine towers can be critical during the installation phase, when the rotor-nacelle assembly is not yet mounted on the tower. The present work uses numerical simulations to study VIVs of a two-dimensional cylinder in the transverse direction under flow conditions that are representative of wind turbine towers both from a fluid dynamics and structural dynamics perspective. First, the numerical tools and fluid-structure interaction algorithm are validated by considering a cylinder vibrating freely in a laminar flow. In that case, both the motion amplitude and frequency are shown to agree well with previous results from the literature. Second, VIVs are modelled in the turbulent supercritical regime using unsteady Reynolds-averaged Navier-Stokes equations. In this context, the turbulence model is first validated against flow past a stationary cylinder with a high Reynolds number. Then, the results from forced vibrations are validated against experimental results for a range of reduced frequencies and velocities. It is shown that the behaviour of the aerodynamic damping changes with the frequency ratio and can therefore lead to either self-limiting or self-exciting VIVs when the cylinder is left to freely vibrate. Finally, results are shown for a freely vibrating cylinder under realistic flow and structural conditions. While a clear lock-in map is identified and shows good agreement with published numerical and experimental data, the work also highlights the unsteady nature of the aerodynamic forces and motion under certain operating conditions..