Abstract
The structure of the internal boundary layer above long wind farms is investigated experimentally. The transfer of kinetic energy from the region above the farm is dominated by the turbulent flux of momentum together with the displacement of kinetic energy operated by the mean vertical velocity: these two have comparable magnitude along the farm opposite to the infinite-farm case. The integration of the energy equation in the vertical highlighted the key role of the energy flux, and how that is balanced by the growth of the internal boundary layer in terms of energy thickness with a small role of the dissipation. The mean velocity profiles seem to follow a universal structure in terms of velocity deficit, while the Reynolds stress does not follow the same scaling structure. Finally, a spectral analysis along the farm identified the leading dynamics determining the turbulent activity: while behind the first row the signature of the tip vortices is dominant, already after the second row their coherency is lost and a single broadband peak, associated with wake meandering, is present until the end of the farm. The streamwise velocity peak is associated with a nearly constant Strouhal number weakly dependent on the farm layout and free stream turbulence condition. A reasonable agreement of the velocity spectra is observed when the latter are normalised by the velocity variance and integral time scale: nevertheless the spectra show clear anisotropy at the large scales and even the small scales remain anisotropic in the inertial subrange.
Highlights
Worldwide efforts are carried out to reduce our dependence on fossil fuels due to their harmful effects on the environment and their non-renewable character
While onshore wind farms follow a layout driven by the terrain to exploit the eventual speedups, offshore farms are limited by the feasible locations where the sea depth is neither too shallow nor too deep, enabling the construction of the foundation and the installation of the turbines
It is quite remarkable that the tower leaves a significant footprint downwind of the turbine, despite its small size compared with the rotor, but it has a profound effect in both the mean velocity and the standard deviation, with a intensity comparable with the tip vortices at the closest plane
Summary
Worldwide efforts are carried out to reduce our dependence on fossil fuels due to their harmful effects on the environment and their non-renewable character. The problem was approached from another (‘top-down’) direction where the wind turbines in a large array are modelled as surface roughness elements, leading to an increased roughness length that needs to be parameterised This idea was introduced by Newman (1977) and Lissaman (1979) and further developed by Frandsen (1992) and Frandsen et al (2006) who proposed a one-dimensional, single-column-type model that replaced the complex three-dimensional structure of a wind farm with a horizontal average often used to describe turbulent flows in canopies (Raupach & Shaw 1982; Raupach, Coppin & Legg 1986; Raupach, Finnigan & Brunet 1996; Yang et al 2006; Segalini, Fransson & Alfredsson 2013).
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