The Statistical Distribution of Turbulence Driven Velocity Extremes in the Atmosperic Boundary Layer cartwright/Longuet-Higgins Revised

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The statistical distribution of extreme wind excursions above a mean level, for a specified recurrence period, is of crucial importance in relation to design of wind sensitive structures. This is particularly true for wind turbine structures. Based on an assumption of a Gaussian "mother" distribution, Cartwright and Longuet-Higgens [1] derived an asymptotic expression for the distribution of the largest excursion from the mean level during an arbitrary recurrence period. From its inception, this celebrated expression has been widely used in wind engineering (as well as in off-shore engineering) - often through definition of the peak factor, which equate the mean of the Cartwright/Longuet-Higgens asymptotic distribution. However, investigations of full scale wind speed time series, recorded in the atmospheric boundary layer, has revealed that the Gaussian assumption is inadequate for events associated with large excursions from the mean [2]. Thus, the more extreme turbulence excursions (i.e. the upper tail of the turbulence PDF) seem to follow an Exponential-like distribution rather than a Gaussian distribution, and a Gaussian estimate may under-predict the probability of large turbulence excursions by more than one decade, which is obviously unfortunate in relation to modelling of an asymptotic extreme distribution based on a Gaussian "mother" distribution. The potential problems with applying the Cartwright/Longuet-Higgens distribution to describe extreme gust events, related to wind speeds in the atmospheric boundary layer, is further stressed by the fact, that many extreme value investigations of wind speed gusts (e.g. [3], [4], [5]) have shown, that observed extreme values are well/excellently described the Gumbel EV1 distribution, which, on the other hand, differ from the asymptotic Cartwright/Longuet-Higgens expression. The present paper presents an asymptotic expression for the distribution of the largest excursion from the mean level, during an arbitrary recurrence period, based on a "mother" distribution that reflects the Exponential-like distribution behaviour of large wind speed excursions. This is achieved on the expence of an acceptable distribution fit in the data population regime of small to medium excursions which, however, for an extreme investigation is unimportant. Further, the derived asymptotic distribution is shown to equal a Gumbel EV1 distribution, and the two distribution parameters are expressed as simple functions of the basic parameters characterizing the stochastic wind speed process in the atmospheric boundary layer. Finally, model predictions of the derived model are compared to predictions from the Cartwright/Longuet-Higgens model as well as to results derived from full-scale measurements of wind speeds in the atmospheric boundary layer.
Original languageEnglish
Title of host publicationWind Energy : Proceedings of the Euromech Colloquium
Number of pages332
Place of PublicationBerlin
PublisherSpringer Verlag
Publication date2007
ISBN (Print)978-3-540-33865-9
Publication statusPublished - 2007
EventEUROMECH Colloquium 464b: Wind Energy: International Colloquium on Fluid Mechanics and Mechanics of Wind Energy Conversion - University of Oldenburg, Oldenburg, Germany
Duration: 4 Oct 20057 Oct 2005


ConferenceEUROMECH Colloquium 464b: Wind Energy
LocationUniversity of Oldenburg
Internet address

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