Streamwise inhomogeneity of spectra and vertical coherence of turbulent motions in a finite-size wind farm

This paper examines the streamwise-inhomogeneous nature of turbulence in a finite-size developing wind farm. While previous analysis involving Fourier spectra revealed an interesting dynamics showing a dominance of the large-scale motions on the order of ten rotor diameters in the energetics of fully developed wind farms [T. Chatterjee and Y. T. Peet, Phys. Rev. Fluids 3, 034601 (2018)2469-990X10.1103/PhysRevFluids.3.034601], harmonic analysis methods do not capture the streamwise variability of spectra, especially important in strongly inhomogeneous flows such as a developing wind farm turbulence. The current study uses wavelet analysis of large eddy simulation data to investigate the turbulent spectra with respect to its spatial position along the wind farm. The analysis shows that the correlation length scales grow significantly past the first row of wind turbines, testifying to a strengthening of the large-scale motions by wind turbines. A vertical coherence of streamwise and vertical velocity fluctuations is also found to increase significantly past the first row of turbines, associated with the development of a global energy transfer mechanism between the outer layer and the wind turbine region. While this mechanism, known as a downdraft of kinetic energy, was previously discussed in the context of fully developed wind farms, the current study illustrates a signature of its origination after as early as the first row of wind turbines. Understanding of the mechanisms responsible for the reorganization of motions of different scales in wind farm flows is useful for designing efficient wind farm control strategies and mitigating the effects of the downstream wakes.