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The neutrinos emitted from the proto-neutron star created in a core-collapsesupernova must run through a significant amount of turbulence before exitingthe star. Turbulence can modify the flavor evolution of the neutrinosimprinting itself upon the signal detected here at Earth. The turbulence effectupon individual neutrinos, and the correlation between pairs of neutrinos,might exhibit sensitivity to the power spectrum of the turbulence and recentanalysis of the turbulence in a two-dimensional hydrodynamical simulation of acore-collapse supernova indicates the power spectrum may not be the Kolmogorov5/3 inverse power law as has been previously assumed. In this paper we studythe effect of non-Kolmogorov turbulence power spectra upon neutrinos from apoint source as a function of neutrino energy and turbulence amplitude at afixed post-bounce epoch. We find the two effects of turbulence upon theneutrinos - the distorted phase effect and the stimulated transitions - bothpossess strong and weak limits in which dependence upon the power spectrum isabsent or evident respectively. Since neutrinos of a given energy will exhibitthese two effects at different epochs of the supernova each with evolvingstrength, we find there is sensitivity to the power spectrum present in theneutrino burst signal from a Galactic supernova.

Supernova neutrinos and the turbulence power spectrum: point source statistics