In the wind energy industry there is a growing need for real-time predictions of wind turbine wake flows in order to optimize power plant control and inhibit detrimental wake interactions. To this aim, a data-driven RANS approach is proposed in order to achieve very low computational costs and adequate accuracy through the data assimilation procedure. The RANS simulations are implemented with a classical Boussinesq hypothesis and a mixing length turbulence closure model, which is calibrated through the available data. High-fidelity LES simulations of a utility-scale wind turbine operating with different tip speed ratios are used as database. It is shown that the mixing length model for the RANS simulations can be calibrated accurately through the Reynolds stress of the axial and radial velocity components, and the gradient of the axial velocity in the radial direction. It is found that the mixing length is roughly invariant in the very near wake, then it increases linearly with the downstream distance in the diffusive region. The variation rate of the mixing length in the downstream direction is proposed as a criterion to detect the transition between near wake and transition region of a wind turbine wake. Finally, RANS simulations were performed with the calibrated mixing length model, and a good agreement with the LES simulations is observed.