A new analytical model for wind turbine wakes based on Monin-Obukhov similarity theory

The wake flow behind a wind turbine induces a significant slowdown of wind velocity, leading to a great loss of power generation for the turbines located in the downstream region. Hence it is very important to predict the velocity in an efficient way. To satisfy this requirement, we propose a simple analytical wake model based on the Monin-Obukhov similarity theory. The new model adopts a Gaussian function and takes surface roughness length and Obukhov length into account for the first time. Then the model is validated from the following three aspects. Firstly, compared with experimental and numerical data, it is shown that the model can present a satisfactory prediction of the ambient turbulence intensities in three spatial directions and the wake expansion parameters. In addition, wind velocity deficits in the wake calculated by the model are compared with the LES data and the Lidar measurements. The results indicate that there is a good agreement with the referenced data. Finally, wake expansion parameters and wind velocity deficits are estimated for three atmospheric stabilities and compared with high resolution LES results. Even though some predicting errors exist in near wakes and for low incoming turbulence intensities, acceptable results are achieved in most of the regions of the wake. Overall speaking, roughness length and atmospheric stability have a great impact on ambient turbulence intensity, which significantly influences the velocity recovery speed in the wind turbine wake.