  In this second communication we continue our analysis of the turbulence in
the Huygens Region of the Orion Nebula (M 42). We calculate the associated
transverse structure functions up to order 8-th and find that the higher-order
transverse structure functions are almost proportional to the second-order
transverse structure function: we find that after proper normalisation, the
higher-order transverse structure functions only differ by very small
deviations from the second-order transverse structure function in a
sub-interval of the inertial range. We demonstrate that this implies that the
turbulence in the Huygens Region is quasi-log-homogeneous, or to a better
degree of approximation, binomially weighted log-homogeneous in the statistical
sense, this implies that there is some type of invariant statistical structure
in the velocity field of the Huygens Region. We also obtain and analyse the
power-spectrum of the turbulent field and find that it displays a large tail
that follows very approximately two power-laws, one of the form $E(k)\propto
k^{-2.7}$ for the initial side of the tail, and one of the form $E(k)\propto
k^{-1}$ for the end of the tail. We find that the power-law with exponent
$\beta\sim -2.7$ corresponds to spatial scales of 0.0301--0.6450 pc. We find
that the exponent of the first power-law $\beta\sim -2.7$ is related to the
exponent $\alpha_2$ of the second-order structure function in the inertial
range. We interpret the second power-law with exponent $\beta \sim -1$ as an
indicator of viscous-dissipative processes occurring at scales of $\delta
r=1$--5 pixels which correspond to spatial scales of 0.00043--0.00215 pc.
