Laser Doppler velocimetry measurements and computational fluid dynamic (CFD) simulations of turbulent flows with free-surface vortex in an unbaffled dish-bottom stirred tank reactor agitated by a Rushton turbine are presented. Measurements of the three mean and fluctuating components of the velocity vector are made in order to characterise the flow field and to provide data for CFD model validation. An Eulerian-Eulerian multiphase flow model coupled with a volume-of-fluid method for capturing the gas-liquid interface is applied to determine the vortex shape and to compute the flow field. Turbulence is modelled using the standard k-e, shear-stress transport and the differential Reynolds-stress model with two variants of the pressure-strain correlation. The predicted mean flow field obtained using all four turbulence models are on the whole similar and generally in good agreement with measurements. However, the Reynolds-stress models provide somewhat better predictions of the mean axial velocity. The turbulent kinetic energy is well predicted in the flow below the impeller, near the bottom of the tank; whereas it is underpredicted in the region close to the impeller and near the wall by all turbulence models.