A Model for Low-Frequency, Anisotropic Wind Fluctuations and Coherences in the Marine Atmosphere

Abstract

To assess dynamic loads, large offshore wind turbines need detailed and reliable statistical information on the inflow turbulence. We present a model that includes low frequencies down to ∼1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 1$$\\end{document} hr-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document} using the observed S(f)∝f-5/3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S(f) \\propto f^{-5/3}$$\\end{document} in that range. The presented model contains a parameter representing the anisotropy of the two-dimensional, incompressible turbulence, and it assumes the low-frequency fluctuations to be homogeneous in the vertical direction. Combined with a three-dimensional model for the smaller scales, the model can predict correlations between different points. We have validated the model against two offshore wind data sets: a nacelle-mounted, forward-looking Doppler lidar with four beams at the Hywind Scotland offshore wind farm and sonic anemometer measurements at the FINO1 research platform in the North Sea. One-point auto spectra and two-point cross spectra were calculated after splitting the data into different atmospheric stability classes. The relative strength of the 2D low-frequency fluctuations to the 3D fluctuations was higher under stable conditions. The combined 2D+3D model was able to fit the measured spectra with good accuracy and could then predict the two-point cross spectra, co-coherences, and phase angles between wind fluctuations at different lateral and vertical separations. Good agreement was found between the measured and predicted values, albeit with exceptions. The model can generate stochastic wind fields for investigating wake meandering in wind farms or dynamic loads on floating wind turbines.