Analytical wind turbine wake models are widely used to predict the wake velocity deficit. In these models, the wake growth rate is a key parameter specified mainly with empirical formulations. In this study, a new physics-based model is proposed and validated to predict the wake expansion downstream of a turbine based on the incoming ambient turbulence and turbine operating conditions. The new model utilises Taylor diffusion theory, the Gaussian wake model, turbulent mixing layer theory and the analogy between wind turbine wake expansion and scalar diffusion. These components ensure that the model conserves mass and momentum in the far wake and accounts for the ambient turbulence and turbine-induced turbulence effects on the wake expansion. To account for the turbulence relevant scales that contribute to the wake expansion, the model uses the root-mean-square of the low-pass filtered radial velocity component. A simplified version that only requires the unfiltered velocity standard deviation and turbulence integral scale is also proposed. In addition, a new relation for the near-wake length is derived. The model performance is validated using large-eddy simulation data of a wind turbine wake under neutral atmospheric conditions with a wide range of incoming turbulence levels. The results show that the proposed model yields reasonable predictions of the wake width, maximum velocity deficit and near-wake length. In the case with a relatively low incoming streamwise turbulence intensity of 0.05, the ambient and turbine-induced terms in the model contribute almost equally to the wake width, rendering them both crucial for reasonable wake predictions.

In this study, we aim to investigate if there is a scaling of the streamwise distance from a wind turbine that leads to a collapse of the mean wake velocity deficit under different ambient turbulence levels. For this purpose, we perform large-eddy simulations of the wake of a wind turbine under neutral atmospheric conditions with various turbulence levels. Based on the observation that a higher atmospheric turbulence level leads to faster wake recovery and shorter near-wake length, we propose the use of the near-wake length as an appropriate normalization length scale. By normalizing the streamwise distance by the near-wake length, we obtain a collapse of the normalized wake velocity deficit profiles for different turbulence levels. We then explore the possibility of using the relationship obtained for the normalized maximum wake velocity deficit as a function of the normalized streamwise distance in the context of analytical wake modeling. Specifically, we investigate two approaches: (a) using the new relationship as a stand-alone model to calculate the maximum wake velocity deficit, and (b) using the new relationship to calculate the wake advection velocity within a physics-based wake expansion model. Large-eddy simulation of the wake of a wind turbine under neutral atmospheric conditions is used to evaluate the performance of both approaches. Overall, we observe good agreement between the simulation data and the model predictions, along with considerable savings in terms of the models’ computational costs.