Large wind farm power and turbine yaw: insights from turbulent boundary layer and vortex structure fundamentals

In this presentation we examine the question of wind energy power density and wind farm flow structure from the viewpoint of basic turbulent boundary layer physics. We restrict attention to near-neutral atmospheric conditions and consider the limit of very large wind farms on flat terrains or off-shore.  We show how generalized logarithmic velocity profiles can be used to enhance our understanding of wind power density. We  then go on to show how simple lifting line theory can be applied to greatly improve on models for yawed wind turbine wakes. Effects of vortex decay due to turbulent diffusion are discussed and we show how to include such effects in simple analytical models for the velocity distribution in wakes. Effects of wind veer are also described. Finally, we summarize efforts to couple local and global boundary layer effects in new-generation wind farm models. The work to be presented arose from the contributions of C. Shapiro (now DOE), G. Starke (now NREL), D. Gayme (JHU), G. Narasimhan (JHU), M. Bastankhah (Durham, UK), S. Shamsoddin (Zürich, CH), M. Howland (now MIT), also based on earlier work with R. Stevens (Twente U, NL), M. Calaf (Utah), and J. Meyers (Leuven, B). We are grateful to the US National Science Foundation for financial support.