  The extent to which turbulence mixes gas in the face of recurrent infusions
of fresh metals by supernovae (SN) could help provide important constraints on
the local star formation conditions. This includes predictions of the
metallicity dispersion amongst metal poor stars, which suggests that the
interstellar medium was not very well mixed at these early times. The purpose
of this {\it Letter} is to help isolate, via a series of numerical experiments,
some of the key processes that regulate turbulent mixing of SN elements in
galactic disks. We study the gas interactions in small simulated patches of a
galaxy disk with the goal of resolving the small-scale mixing effects of metals
at pc scales, which enables us to measure the turbulent diffusion coefficient
in various galaxy environments. By investigating the statistics of variations
of $\alpha$ elements in these simulations, we are able to derive constraints
not only on the allowed range of intrinsic yield variations in SN explosions
but also on the star formation history of the Milky Way. We argue that the
observed dispersion of [Mg/Fe] in metal poor halo stars is compatible with the
star-forming conditions expected in dwarf satellites or in an early low
star-forming Milky Way progenitor. In particular, metal variations in stars
that have not been phase-mixed can be used to infer the star-forming conditions
of disrupted dwarf satellites.
