Optimal turbine spacing in fully developed wind farm boundary layers

As wind farms become larger, the asymptotic limit of the fully developed, or infinite, wind farm has been receiving an increased interest. This limit is relevant for wind farms on flat terrain whose length exceeds the height of the atmospheric boundary layer by over an order of magnitude. Recent computational studies based on large eddy simulation have identified various mean velocity equilibrium layers and have led to parameterizations of the effective roughness height that allow the prediction of the wind velocity at hub height as a function of parameters such as wind turbine spacing and loading factors. In the current paper, we employ this as a tool in making predictions of optimal wind turbine spacing as a function of these parameters, as well as in terms of the ratio of turbine costs to land surface costs. For realistic cost ratios, we find that the optimal average turbine spacing may be considerably higher than that conventionally used in current wind farm implementations. Copyright (C) 2011 John Wiley & Sons, Ltd.