Graduate Thesis Or Dissertation
 

The influence of small scale variability on scaling relationships describing atmospheric turbulence

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  • The statistics describing variations of turbulent motions within the so called inertial range of length scales depend on the scale over which the motions are varying and the "average" rate at which the turbulent kinetic energy is being dissipated on the molecular scale. This hypothesis stemmed from the similarity arguments published by A. N. Kolmogorov in 1941 and implies specific scaling relations between the average amplitude and length scale of turbulent motions. Turbulent motions agree to a good approximation with Kolmogorov scaling provided the fluid flow admits to the underlying assumptions. More recently it has been recognized that the large spatial variations in the rate of turbulent kinetic energy dissipation may be a partial explanation for deviations from Kolmogorov scaling. This recognition is due in part to the observation that the total volume occupied by turbulent motions of a given scale decreases as the scale decreases. These observations imply that active small scale turbulence is intermittent. This study aims to better understand how scaling relations describing more active regions are different from the relations describing turbulence where the small scales are less active. The thesis is that the relations are different. An 18 hour segment of wind data measured in near-neutral stratification 45 meters above a relatively flat ground is analyzed. There is virtually no trend in the mean wind speed, so the describing statistics are essentially stationary. Small scale activity is measured in terms of the difference in wind speed (structure function) at a separation distance of 1/16 of a second, which translates to about a meter. The differences in wind speed are raised to the sixth power and then averaged over 4 second (50 meter) windows. Non-overlapping windows containing a local maximum in the averaged sixth order structure function form one (MASC) ensemble of more active small scale samples and the local minima form another (LASC) ensemble of less active small scale samples. The variations in wind speed as a function of length scale within each ensemble are decomposed five different ways. Each of the five decompositions obey scaling relationships that are approximately linear in log-log coordinates. The MASC and LASC ensembles include 32% and 46% of the record, respectively. The turbulent kinetic energy as a function of scale falls off at a slower rate in the MASC ensemble versus the LASC ensemble and in magnitude the energy is greater at all scales in the MASC ensemble. This implies the transfer rate of turbulent kinetic energy toward small scales is more rapid on average in the MASC samples. Samples in the MASC ensemble occupied 30% less of the record, implying the flattening effect on the spectral slope exhibited by the samples contained in the MASC ensemble is less influential than the steepening influence of samples of the type in the LASC ensemble. The results are robust with respect to the choice of a basis set in representing the variance as a function of scale.
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