WESD Wind Energy Science Discussions WESD Wind Energ. Sci. Discuss. 2366-7621 Göttingen, Germany 10.5194/wes-2021-21 An analytical solution for wind deficit decay behind a wind energy converter using momentum conservation validated by UAS data Mauz Moritz https://orcid.org/0000-0003-0801-9438 1 van Kesteren Bram 1 Platis Andreas https://orcid.org/0000-0002-9276-3587 1 Emeis Stefan https://orcid.org/0000-0001-6114-6212 2 Bange Jens https://orcid.org/0000-0003-4075-1573 1 Centre for Applied Geoscience, University of Tübingen, 72074 Tübingen, Germany Institute for Meteorology and Climate Research, Karlsruhe Institute of Technology, 82467 Garmisch-Partenkirchen, Germany 15 03 2021 2021 1 24 Copyright: © 2021 Moritz Mauz et al. 2021 This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/ This article is available from https://wes.copernicus.org/preprints/wes-2021-21/ The full text article is available as a PDF file from https://wes.copernicus.org/preprints/wes-2021-21/wes-2021-21.pdf

<p>The wind deficit behind a wind energy converter (WEC) results from a complex interaction of forces. Kinetic energy is removed from the atmosphere, but coherent turbulent structures prevent a swift compensation of momentum within the wake behind the WEC. A detailed description of the wake is beneficial in meso-scale weather forecast (e.g. WRF models) and numerical simulations of wind wake deficits. Especially in the near to intermediate wake (0.5−5 rotor diameters D), the dominating processes characterising the wake formation change along the wake. The conservation equation of momentum is used as a starting point to map the most important processes assuming the WEC operates at maximum efficiency in a neutral stratified boundary layer. The wake is divided into three different regions to accommodate the changing impact of atmospheric turbulence and the shear created by the WEC onto the wake. A differential equation that depicts the variable momentum transport into the wind deficit along the wake is derived and solved analytically. Additionally, a numerical solution (Euler method) of the simplified momentum conservation equation is shown to provide a quality control and error estimate to the analytical model. The analytical solution is compared to conventional WEC wake models and in-situ wake measurements behind an Enercon E-112 converter, located in the Jade Wind Park near the North Sea coast in Germany, captured by the MASC-3 UAS (unmanned aircraft system) of the University of Tübingen. The obtained UAS data cover the distance from 0.5−5 D at hub height behind the nacelle. The analytical and numerical model are found to be in good agreement with the data of the three measurement flights behind the WEC.</p>