Boundary-Layer Meteorology

, Volume 169, Issue 1, pp 1–10 | Cite as

A Simple Physically-Based Model for Wind-Turbine Wake Growth in a Turbulent Boundary Layer

  • Wai-Chi Cheng
  • Fernando Porté-Agel
Research Letter


The growth rate of wind-turbine wakes in the atmospheric boundary layer is a key parameter in analytical models used to predict wind-turbine wakes and their effects in wind farms. To date, the turbine-wake growth rate is determined empirically, owing to our limited understanding of the physical mechanisms leading to the recovery of the wakes in turbulent flows. Here, a simple physically-based model for wind-turbine wake growth is proposed based on the analogy with scalar dispersion in turbulent flows. The model is developed based on Taylor’s diffusion theory and intrinsically accounts for the effect of ambient turbulence intensity. In validations against large-eddy simulations of the wake flow of a turbine under different inflow turbulence conditions, it is found that the model yields good predictions of the growth of the turbine wakes. A slight underestimation of the wake growth rate is found only in the lowest ambient turbulence case, due to the non-negligible contribution of the turbine-induced turbulence in that case.


Velocity deficit Wake growth rate Wind-turbine wake 



This research was supported by the Swiss National Science Foundation (Grant No. 2000215\(\_\)172538), the Swiss Federal Office of Energy (Grant No. SI/501337-01), and the Swiss Innovation and Technology Committee (CTI) within the context of the Swiss Competence Center for Energy Research “FURIES: Future Swiss Electrical Infrastructure”.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Wind Engineering and Renewable Energy Laboratory (WIRE)École Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland

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