Abstract
Atmospheric wind speeds and their fluctuations at different locations (onshore and offshore) are examined. One of the most striking features is the marked intermittency of probability density functions (PDF) of velocity differences, no matter what location is considered. The shape of these PDFs is found to be robust over a wide range of scales which seems to contradict the mathematical concept of stability where a Gaussian distribution should be the limiting one. Motivated by the non-stationarity of atmospheric winds it is shown that the intermittent distributions can be understood as a superposition of different subsets of isotropic turbulence. Thus we suggest a simple stochastic model to reproduce the measured statistics of wind speed fluctuations.
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Notes
In the following the term ‘isotropic turbulence’ instead of ‘homogeneous, isotropic and stationary turbulence’ will be used.
Normally Θ and T denote length scales. For constant mean velocities and applying Taylor’s hypothesis of frozen turbulence length can be defined as time-scales as well. Here we will proceed with corresponding time scales.
The differential probability to observe an increment u τ ε [u τ′ u τ + du τ] is just given by p(u τ) du τ.
Eq. 7 and other multifractal models yield very similar results because such low-order exponents as ζ4 and ζ2 are quite indistinguishable from each other.
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Acknowledgments
We acknowledge helpful discussions with M. Siefert and B. Lange. For data supply we further acknowledge Risø National Laboratory (offshore site funded by Energi E2/Seas), Tauernwind Windkraftanlagen GmbH, Energiewerkstatt GmbH, J. Cleve and K. R. Sreenivasan.
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Böttcher, F., Barth, S. & Peinke, J. Small and large scale fluctuations in atmospheric wind speeds. Stoch Environ Res Ris Assess 21, 299–308 (2007). https://doi.org/10.1007/s00477-006-0065-2
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DOI: https://doi.org/10.1007/s00477-006-0065-2