  During the shock-wave propagation in a core-collapse supernova (SN), matter
turbulence may affect neutrino flavor conversion probabilities. Such effects
have been usually studied by adding parametrized small-scale random
fluctuations (with arbitrary amplitude) on top of coarse, spherically symmetric
matter density profiles. Recently, however, two-dimensional (2D) SN models have
reached a space resolution high enough to directly trace anisotropic density
profiles, down to scales smaller than the typical neutrino oscillation length.
In this context, we analyze the statistical properties of a large set of SN
matter density profiles obtained in a high-resolution 2D simulation, focusing
on a post-bounce time (2 s) suited to study shock-wave effects on neutrino
propagation on scales as small as O(100) km and possibly below. We clearly find
the imprint of a broken (Kolmogorov-Kraichnan) power-law structure, as
generically expected in 2D turbulence spectra. We then compute the flavor
evolution of SN neutrinos along representative realizations of the turbulent
matter density profiles, and observe no or modest damping of the neutrino
crossing probabilities on their way through the shock wave. In order to check
the effect of possibly unresolved fluctuations at scales below O(100) km, we
also apply a randomization procedure anchored to the power spectrum calculated
from the simulation, and find consistent results within \pm 1 sigma
fluctuations. These results show the importance of anchoring turbulence effects
on SN neutrinos to realistic, fine-grained SN models.
