  Atomic cooling haloes with virial temperatures $\rm T_{vir} \geq 10^{4}$ K
are the most plausible sites for the formation of the first galaxies and the
first intermediate mass black holes. It is therefore important to assess
whether one can obtain robust results concerning their main properties from
numerical simulations. A major uncertainty is the presence of turbulence, which
is barely resolved in cosmological simulations. We explore the latter both by
pursuing high-resolution simulations with up to 64 cells per Jeans length and
by incorporating a subgrid-scale turbulence model to account for turbulent
pressure and viscosity on unresolved scales. We find that the main physical
quantities in the halo, in particular the density, temperature and energy
density profile, are approximately converged. However, the morphologies in the
central 500 AU change significantly with increasing resolution and appear
considerably more turbulent. In a systematic comparison of three different
haloes, we further found that the turbulence subgrid-scale model gives rise to
more compact central structures, and decreases the amount of vorticity. Such
compact morphologies may in particular favor the accretion onto the central
object.
