  In order to study the nature, origin, and impact of turbulent velocity
fluctuations in the ionized gas of the Orion Nebula, we apply a variety of
statistical techniques to observed velocity cubes. The cubes are derived from
high resolving power ($R \approx 40,000$) longslit spectroscopy of optical
emission lines that span a range of ionizations. From Velocity Channel Analysis
(VCA), we find that the slope of the velocity power spectrum is consistent with
predictions of Kolmogorov theory between scales of 8 and 22 arcsec (0.02 to
0.05 pc). The outer scale, which is the dominant scale of density fluctuations
in the nebula, approximately coincides with the autocorrelation length of the
velocity fluctuations that we determine from the second order velocity
structure function. We propose that this is the principal driving scale of the
turbulence, which originates in the autocorrelation length of dense cores in
the Orion molecular filament. By combining analysis of the non-thermal line
widths with the systematic trends of velocity centroid versus ionization, we
find that the global champagne flow and smaller scale turbulence each
contribute in equal measure to the total velocity dispersion, with respective
root-mean-square widths of 4-5 km/s. The turbulence is subsonic and can account
for only one half of the derived variance in ionized density, with the
remaining variance provided by density gradients in photoevaporation flows from
globules and filaments. Intercomparison with results from simulations implies
that the ionized gas is confined to a thick shell and does not fill the
interior of the nebula.
