A two-dimensional Jensen model with a Gaussian-shaped velocity deficit

The one-dimensional (1D) Jensen model is probably the most often used model for engineering analysis of wind turbine wakes. Identifying a more realistic shape function for the near and far wakes behind a wind turbine and incorporating the identified shape function into a wake model can significantly improve the accuracy of wake modelling. The conventional approach is to first solve the 1D Jensen model and subsequently redistribute the wake using a specified shape function. The above procedure conserves mass globally and is useful in wake modelling. However, it needs to solve a top-hat wake using Jensen model first, which inevitably violates the local mass conservation. In this work, we propose a two-dimensional (2D) wake model that conserves mass locally and globally. The model is a direct extension of Jensen model, and the wake decay rate is the only model parameter. In addition, by accounting for the pressure recovery region, which is often neglected in wake models, the present model can provide accurate prediction of the velocity deficit behind a wind turbine. The present model is compared with the high-fidelity simulations, wind-tunnel measurements, and field observations. A reasonably good agreement is found between the model and the validation data.