Abstract
We study the turbulent regime of chiral (magneto)hydrodynamics for charged and neutral matter with chirality imbalance. We find that the chiral magnetohydrodynamics for charged plasmas possesses a unique scaling symmetry, only without fluid helicity under the local charge neutrality. We also find a different type of unique scaling symmetry in the chiral hydrodynamics for neutral matter with fluid helicity in the inertial range. We show that these symmetries dictate the self-similar inverse cascade of the magnetic and kinetic energies. Our results imply the possible inverse energy cascade in core-collapse supernovae due to the chiral transport of neutrinos.
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