### Abstract:

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.