  Multi-dimensional core-collapse supernova simulations exhibit turbulence of
large amplitude and over large scales. As neutrinos pass through the supernova
mantle the turbulence is expected to modify their evolution compared to the
case where the explosion is free of turbulence. In this paper we study this
turbulence effect upon the neutrinos modelling the turbulence expected from
multi-dimensional simulations by adding matter density fluctuations to density
profiles taken from one-dimensional hydrodynamical simulations. We investigate
the impact upon the supernova neutrino transition probabilities as a function
of the neutrino mixing angle theta_13 and turbulence amplitude. In the high (H)
resonant channel and with large theta_13 values we find that turbulence is
effectively two flavor for fluctuation amplitudes <~ 1% and have identified a
new effect due to the combination of turbulence and multiple H resonances that
leads to a sensitivity to fluctuations amplitudes as small as ~ 0.001%. At
small values of theta_13, beyond the range achievable in Earth based
experiments, we find that turbulence leads to new flavor transient effects in
the channel where the MSW H resonance occurs. Finally, we investigate large
amplitude fluctuations which lead to three flavor effects due to broken HL
factorization and significant non-resonant transitions and identify two
non-resonant turbulence effects, one depending on the theta_13, and the other
independent of this angle and due to the low (L) MSW resonance.

High Energy Physics - Phenomenology;High Energy Astrophysical Phenomena