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()Banelle I~ b DISCLAI MERThis repo rt was p repared as an acco un t of work spo nsore d by an agency o f the Uni ted States Govern ment. Neither the Un ited States Gove rnm en t nor any age ncy th ereo f, nor an y of thei r employees, mak es any w ar ra n ty, ex press or im p lied , o r assu mes any legal liab i lity or respo nsib i li ty for the accuracy, comp letene ss, or usefu lness of any infor ma ti o n, appa ratu s, pro d uct , or process disc losed , or re p resents t hat its use wo u ld no t infri nge pri vately ow ned right s. A theoretical model is modified and tested that produces the power spectrum of the alongwind component of turbulence as experienced by a point rotating in a vertical plane perpendicular to the mean wind direction. The ability to generate such a power spectrum, independent of measurement, is important in wi nd turbine design and testing. The radius of the circle of rotation, its height above the ground, and the rate of rotation are typical for those for a MOO-OA wind turbine. Verification of this model is attempted by comparing two sets of variances that correspond to individual harmonic bands of spectra of turbulence in the rotational frame. One set of variances is calculated by integrating the theoretically generated rotational spectra; the other is calculated by integrating rotational spectra from real data analysis. The theoretical spectrum is generated by Fourier transformation of an autocorrelation function taken from von Karman and modified for the rotational frame. The autocorrelation is based on dimensionless parameters, each of which incorporates both atmospheric and wind turbine parameters. The real data time series are formed by sampling around the circle of anemometers of the Vertical Plane Array at the former ~100-0A site at Clayton, New Mexico.Three time series were selected from data taken in a previous study; the time series represent slightly unstable, definitely unstable, and stable atmospheric conditions. All series were analyzed for 8.5-min periods of data. The first series was also analyzed for a 17-min data period.The theoretical model verifies at all frequencies from 1P to 5P with the 8.5-min runs except for the stable case. In all cases the ratios of variance in a harmonic band from the model to the corresponding variance from real data analysis decrease as the harmonic number increases. Since both sets of variances show decreasi ng magnitude with i ncreasi ng harmonic number (from 1P, 2P, ... 5P), variances from the model show a more rapid decrease of energy with harmonic than do the variances from real data analysis. For the slightly unstable case these ratios ran from 1.38 at 1P to 0.83 at 5P. However, the iii decrease of this ratio with frequency could result from noise in the observed data as well as from known and unknown limitations of the theoretical model.The necessary input parameters for the model include the variance as well as both the longitudinal and lateral length scales of u-component turbulence.(The empirical specification of two length ...

This report w as prepared as an accou nt of work sponsored by an agency of the Uni ted States Governm ent. Neither the Un ited States Govern ment nor any agency thereof, nor an y of their em ployees, ma kes an y w arran ty, express or implied, or assu mes any legal liability o r respon sibili ty for the accuracy, comp let eness, or usefu lness of any info rmat ion, ap parat us, p rod uct, or process disclosed , or represents t hat its use wo uld not infrin ge priva tely own ed rights. Reference herein to any specific com merci al p roduct, p rocess, or service by trade na me, trademark , manufactu rer, or otherwise, does not necessarily constit ute or imply its end orse ment, reco mmendat ion , or favo ring by th e U ni te d States Govern ment o r any agency th ereof. The views and opinions of authors expressed herei n do not necessa rily state or reflect those of the United States Govern ment or any agency thereof.

A-4 Frequency S h i f t i n g o f a Spectrum From That Seen by a S t a t i o n a r y Observer t o That Seen by an Observer Moving With a Fixed V e l o c i t y .

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