A Model for the Spectrum of the Lateral Velocity Component from Mesoscale to Microscale and Its Application to Wind-Dire
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A Model for the Spectrum of the Lateral Velocity Component from Mesoscale to Microscale and Its Application to Wind-Direction Variation Xiaoli G. Larsén1
· Søren E. Larsen1 · Erik L. Petersen1 · Torben K. Mikkelsen1
Received: 3 February 2020 / Accepted: 23 September 2020 © Springer Nature B.V. 2020
Abstract A model for the spectrum of the lateral velocity component Sv ( f ) is developed for a frequency range from about 0.2 day−1 to the turbulence inertial subrange, with the intent of improving the calculation of flow meandering over areas the size of offshore wind farms and clusters. These sizes can correspond to a temporal scale of several hours, much larger than the validity limit of typical boundary-layer models, such as the Kaimal model, or the Mikkelsen–Tchen model. The development of the model is based on observations from one site and verified with observations from another site up to a height of 241 m. The model describes three ranges: (1) the mesoscale from 0.2 day−1 to about 10−3 Hz where a mesoscale spectral model from Larsén et al. (2013: QJR Meteorol Soc 139: 685–700) is used; (2) the spectral gap where the normalized v spectrum, f Sv ( f ), can be approximated to be a constant; (3) the high-frequency range where a boundary-layer model is used. In order to demonstrate a general applicability of the lateral velocity spectrum model to reproduce the statistics of wind-direction variability, models for both horizontal velocity components, u and v, are used through an inverse Fourier transform technique to produce time series of both components, which in theory could have been the ensemble for calculating the corresponding spectra. The ensemble is then used to calculate directional statistics, which in turn are compared with corresponding statistics from the measured time series. We demonstrate the relevance of the constructed spectral models for calculating meandering effects for large wind farms and wind-farm clusters. Keywords Spectrum of the lateral velocity component · Mesoscale · Microscale · Meandering
1 Introduction In atmospheric studies of dispersion as well as wind-turbine wakes, meandering is important. It has been consistently suggested that meandering contributes to the overall wind-direction
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Xiaoli G. Larsén [email protected] Wind Energy Department, Risø Campus of the Danish Technical University, Frederiksborgvej 399, 4000 Roskilde, Denmark
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θ change through larger-scale and slow motion. Meandering generally refers to “oscillation of the wind direction back and forth” (Mahrt 2007), and it was observed to be independent of local parameters (Vickers and Mahrt 2007). Anfossi et al. (2005) used observations to study flow characteristics and found that meandering is associated with slow mesoscale motions. Cava et al. (2019) observed that, in the Antarctic stable boundary layer, mesoscale meandering can contribute to the sharp wind-direction changes at low wind speed. In Larsen et al. (2007), the wake-meandering model assumes that the transport of wakes in the atmospheric bo
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