  (Abridged) In order to decode the neutrino burst signal from a Galactic
core-collapse supernova and reveal the complicated inner workings of the
explosion we need a thorough understanding of the neutrino flavor evolution
from the proto-neutron star outwards. The flavor content of the signal evolves
due to both neutrino collective effects and matter effects which can lead to a
highly interesting interplay and distinctive spectral features. In this paper
we investigate the supernova neutrino flavor evolution in three different
progenitors and include collective flavor effects, the evolution of the
Mikheyev, Smirnov & Wolfenstein conversion due to the shock wave passage
through the star, and the impact of turbulence. In the Oxygen-Neon-Magnesium
supernova we find that the impact of turbulence is both brief and slight during
a window of 1-2 seconds post bounce. Thus the spectral features of collective
and shock effects in the neutrino signals from ONeMg supernovae may be almost
turbulence free making them the easiest to interpret. For the more massive
progenitors we again find that small amplitude turbulence, up to 10%, leads to
a minimal modification of the signal, and the emerging neutrino spectra retain
both collective and MSW features. However, when larger amounts of turbulence is
added, 30% and 50%, the features of collective and shock wave effects in the
high density resonance channel are almost completely obscured at late times.
Yet at the same time we find the other mixing channels - the low density
resonance channel and the non-resonant channels - begin to develop turbulence
signatures. Large amplitude turbulent motions in the outer layers of more
massive, iron core-collapse supernovae may obscure the most obvious
fingerprints of collective and shock wave effects in the neutrino signal but
cannot remove them completely, and additionally bring about new features in the
signal.
