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Metal production in galaxies traces star formation, and is highlyconcentrated toward the centers of galactic discs. This suggests that galaxiesshould have inhomogeneous metal distributions with strong radial gradients, butobservations of present-day galaxies show only shallow gradients with littleazimuthal variation, implying the existence of a redistribution mechanism. Westudy the role of gravitational instability-driven turbulence as a mixingmechanism by simulating an isolated galactic disc at high resolution, includingmetal fields treated as passive scalars. Since any cylindrical field can bedecomposed into a sum of Fourier-Bessel basis functions, we set up initialmetal fields characterized by these functions and study how different modesmix. We find both shear and turbulence contribute to mixing, but the mixingstrongly depends on the symmetries of the mode. Non-axisymmetric modes havedecay times smaller than the galactic orbital period because shear winds themup to small spatial scales, where they are erased by turbulence. The decaytimescales for axisymmetric modes are much greater, though for all but thelargest-scale inhomogeneities the mixing timescale is still short enough toerase chemical inhomogeneities over cosmological times. These differenttimescales provide an explanation for why galaxies retain metallicity gradientswhile there is almost no variation at a fixed radius. Moreover, thecomparatively long timescales required for mixing axisymmetric modes mayexplain the greater diversity of metallicity gradients observed in highredshift galaxies as compared to local ones: these systems have not yet reachedequilibrium between metal production and diffusion.

Mixing and transport of metals by gravitational instability-driven turbulence in galactic discs