# A Numerically Efficient Parametrization of Turbulent Wind-Turbine Flows for Different Thermal Stratifications

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## Abstract

The wake characteristics of a wind turbine in a turbulent atmospheric boundary layer under different thermal stratifications are investigated by means of large-eddy simulation with the geophysical flow solver EULAG. The turbulent inflow is based on a method that imposes the spectral energy distribution of a neutral boundary-layer precursor simulation, the turbulence-preserving method. This method is extended herein to make it applicable for different thermal stratification regimes (convective, stable, neutral) by including suitable turbulence assumptions, which are deduced from velocity fields of a diurnal-cycle precursor simulation. The wind-turbine-wake characteristics derived from simulations that include the parametrization result in good agreement with diurnal-cycle-driven wind-turbine simulations. Furthermore, different levels of accuracy are tested in the parametrization assumptions, representing the thermal stratification. These range from three-dimensional matrices of the precursor-simulation wind field to individual values. The resulting wake characteristics are similar, even for the simplest parametrization set-up, making the diurnal-cycle precursor simulation non-essential for the wind-turbine simulations. Therefore, the proposed parametrization results in a computationally fast, simple, and efficient tool for analyzing the effects of different thermal stratifications on wind-turbine wakes by means of large-eddy simulation.

## Keywords

Atmospheric boundary layer Diurnal cycle Large-eddy simulation Turbulence Wind-turbine wake## Notes

### Acknowledgements

The authors thank Fernando Porté-Agel and Gert-Jan Steeneveld for the constructive discussion on the turbulence preserving method. Further, we thank Mark Zagar for providing the airfoil data of the 10-MW reference wind turbine from DTU. This work was performed within the project LIPS, funded by the Federal Ministry of Economy and Energy on the basis of a resolution of the German Bundestag under the contract number 0325518.

### Funding

The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (LRZ, www.lrz.de).

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