A Model for the Spectrum of the Lateral Velocity Component from Mesoscale to Microscale and Its Application to Wind-Direction Variation

Abstract

A model for the spectrum of the lateral velocity component $$S_v(f)$$ is developed for a frequency range from about 0.2 $$\hbox {day}^{-1}$$ 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 $$0.2\ \hbox {day}^{-1}$$ to about $$10^{-3}\ \hbox {Hz}$$ where a mesoscale spectral model from Larsen et al. (2013: QJR Meteorol Soc 139: 685–700) is used; (2) the spectral gap where the normalized v spectrum, $$fS_v(f)$$ , 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.