Assessing the power loss and fatigue in a wind farm due to wake effects requires the use of analytical models for velocity deficit and added turbulence in the wake of turbines. Many steady-state models have been developed in the literature for the velocity deficit, but the added turbulence has received less attention and only an empirical model is available for the whole turbulence profile in the wake of a turbine.

We propose a physically-based model that predicts both the velocity and turbulence in the wake. It accounts for the meandering effect (oscillations of the wake) that is often supposed to only enhance the diffusion in other steady-state models. We show that diffusion and meandering lead to different turbulence profiles and thus need to be modelled separately. Moreover, this separation allows considering the atmospheric stability in the model. A calibration of the model is proposed for neutral and unstable atmospheric conditions. It leads to encouraging results even though it is not yet as performing as the empirical model from the literature.