A model for the spectrum of the lateral velocity component Sv(f)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_v(f)$$\end{document} is developed for a frequency range from about 0.2 day-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {day}^{-1}$$\end{document} 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 0.2day-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.2\ \hbox {day}^{-1}$$\end{document} to about 10-3Hz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{-3}\ \hbox {Hz}$$\end{document} 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, fSv(f)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$fS_v(f)$$\end{document}, 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.

中文翻译：

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中尺度到微尺度横向速度分量谱模型及其在风向变化中的应用

横向速度分量的频谱模型 Sv(f)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{ mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_v(f)$$\end{document} 是为大约 0.2 day-1\documentclass[ 12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {day}^{-1}$$\end{document} 到湍流惯性子范围，目的是改进在离岸风电场和集群大小的区域上蜿蜒流动的计算. 这些大小可以对应几个小时的时间尺度，远大于典型边界层模型的有效性极限，例如 Kaimal 模型或 Mikkelsen-Tchen 模型。该模型的开发基于一个站点的观测，并通过另一站点的观测进行验证，最高高度为 241 m。该模型描述了三个范围：（1）来自 0.2day-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \ usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0. 2\ \hbox {day}^{-1}$$\end{document} 到大约 10-3Hz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{ amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$10^{-3}\ \hbox {Hz}$$\end{文档}，其中来自 Larsén 等人的中尺度光谱模型。(2013: QJR Meteorol Soc 139: 685–700) 被使用；(2) 归一化 v 谱所在的谱间隙，fSv(f)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \ usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$fS_v(f)$$\end{document}，可以近似为一个常数；(3) 使用边界层模型的高频范围。为了证明横向速度谱模型在再现风向变化统计数据方面的普遍适用性，水平速度分量 u 和 v 的模型通过傅立叶逆变换技术用于生成两个分量的时间序列，从理论上讲，这可能是计算相应光谱的集合。然后使用集成来计算方向统计数据，然后将其与测量的时间序列中的相应统计数据进行比较。我们证明了构建的光谱模型对于计算大型风电场和风电场集群的蜿蜒效应的相关性。u 和 v 通过傅里叶逆变换技术产生两个分量的时间序列，理论上这可以是计算相应光谱的集合。然后使用集成来计算方向统计数据，然后将其与测量的时间序列中的相应统计数据进行比较。我们证明了构建的光谱模型对于计算大型风电场和风电场集群的蜿蜒效应的相关性。u 和 v 通过傅里叶逆变换技术产生两个分量的时间序列，理论上这可以是计算相应光谱的集合。然后使用集成来计算方向统计数据，然后将其与测量的时间序列中的相应统计数据进行比较。我们证明了构建的光谱模型对于计算大型风电场和风电场集群的蜿蜒效应的相关性。