  During the accretion phase of a core-collapse supernovae, large amplitude
turbulence is generated by the combination of the standing accretion shock
instability and convection driven by neutrino heating. The turbulence directly
affects the dynamics of the explosion, but there is also the possibility of an
additional, indirect, feedback mechanism due to the effect turbulence can have
upon neutrino flavor evolution and thus the neutrino heating. In this paper we
consider the effect of turbulence during the accretion phase upon neutrino
evolution, both numerically and analytically. Adopting representative supernova
profiles taken from the accretion phase of a supernova simulation, we find the
numerical calculations exhibit no effect from turbulence. We explain this
absence using two analytic descriptions: the Stimulated Transition model and
the Distorted Phase Effect model. In the Stimulated Transition model turbulence
effects depend upon six different lengthscales, and three criteria must be
satisfied between them if one is to observe a change in the flavor evolution
due to Stimulated Transition. We further demonstrate that the Distorted Phase
Effect depends upon the presence of multiple semi-adiabatic MSW resonances or
discontinuities that also can be expressed as a relationship between three of
the same lengthscales. When we examine the supernova profiles used in the
numerical calculations we find the three Stimulated Transition criteria cannot
be satisfied, independent of the form of the turbulence power spectrum, and
that the same supernova profiles lack the multiple semi-adiabatic MSW
resonances or discontinuities necessary to produce a Distorted Phase Effect.
Thus we conclude that even though large amplitude turbulence is present in
supernova during the accretion phase, it has no effect upon neutrino flavor
evolution.
