Application of the Townsend-George theory for free shear flows to single and double wind turbine wakes - a wind tunnel study

The evolution of the mean velocity and the turbulence downstream of wind turbine wakes within the atmospheric boundary layer has been studied over the past decades, but an analytical description is still missing. One possibility to improve the comprehension of this is to look into the modeling of turbulent bluff body wakes. There, by means of the streamwise scaling of the centerline mean velocity deficit, the nature of the turbulence inside a wake can be classified. In this paper, we introduce the analytical model of classical wake theory as introduced by Albert Alan Townsend and William Kenneth George. To test the theories, data were obtained from wind tunnel experiments using hot-wire anemometry in the wakes of a single model wind turbine and a model wind turbine operating in the wake of an upstream model wind turbine. First, we test whether the requirements under which the Townsend-George theory is valid are fulfilled in the wake of a wind turbine. Based on this verification we apply the Townsend-George theory. Further, this framework allows for distinguishing between two types of turbulence, namely equilibrium and non-equilibrium turbulence. We find that the turbulence at the centerline is equilibrium turbulence and that non-equilibrium turbulence may be present at outer parts of the wake. Finally, we apply the Townsend-George theory to characterize the wind turbine wake, and we compare the results to the Jensen and the Bastankhah-Porte-Agel models. We find that the recent developments from the classical bluff body wake formalism can be used to further improve the wind turbine wake models. Particularly, the classical bluff body wake models perform better than the wind turbine wake models due to the presence of a virtual origin in the scalings, and we demonstrate the possibility of improving the wind turbine wake models by implementing this parameter. We also see how the dissipation changes across the wake, which is important to model wakes within wind farms correctly.