  A number of relaxed, cool-core galaxy clusters exhibit diffuse,
steep-spectrum radio sources in their central regions, known as radio
mini-halos. It has been proposed that the relativistic electrons responsible
for the emission have been reaccelerated by turbulence generated by the
sloshing of the cool core gas. We present a high-resolution MHD simulation of
gas sloshing in a galaxy cluster coupled with subgrid simulations of
relativistic electron acceleration to test this hypothesis. Our simulation
shows that the sloshing motions generate turbulence on the order of $\delta{v}
\sim$ 50-200 km s$^{-1}$ on spatial scales of $\sim$50-100 kpc and below in the
cool core region within the envelope of the sloshing cold fronts, whereas
outside the cold fronts, there is negligible turbulence. This turbulence is
potentially strong enough to reaccelerate relativistic electron seeds (with
initial $\gamma \sim 100-500$) to $\gamma \sim 10^4$ via damping of
magnetosonic waves and non-resonant compression. The seed electrons could
remain in the cluster from, e.g., past AGN activity. In combination with the
magnetic field amplification in the core, these electrons then produce diffuse
radio synchrotron emission that is coincident with the region bounded by the
sloshing cold fronts, as indeed observed in X-rays and the radio. The result
holds for different initial spatial distributions of preexisting relativistic
electrons. The power and the steep spectral index ($\alpha \approx 1-2$) of the
resulting radio emission are consistent with observations of minihalos, though
the theoretical uncertainties of the acceleration mechanisms are high. We also
produce simulated maps of inverse-Compton hard X-ray emission from the same
population of relativistic electrons.
