Theoretically optimal turbine resistance in very large wind farms

In this paper we further investigate and validate the novel theoretical model of very large wind farms proposed recently by Nishino (J. Phys.: Conf. Ser. 753, 032054, 2016). One of the key features of the Nishino model is that a theoretically optimal turbine resistance (as well as optimal 'turbine-scale' and 'farm-scale' wind speed reduction rates) can be predicted analytically as a function of the farm density and the natural bottom friction observed before constructing the farm. To validate this theoretical model, a new set of 3D Reynolds-averaged Navier-Stokes (RANS) simulations are performed of a fully developed wind farm boundary layer over an aligned and staggered array of actuator discs with various disc resistance, inter-disc spacing and bottom roughness values. The results show that the theoretical model, which employs only one empirical model parameter, can be easily calibrated to predict very well the performance of various staggered arrays of actuator discs. This suggests the usefulness of the theoretical model not only for providing an upper limit to the performance of ideal large arrays but also for predicting the performance of realistic large arrays. The results also highlight the important fact that the optimal turbine resistance can be significantly smaller in a dense wind farm than in a sparse wind far