  Recent Chandra X-ray observations of many galaxy clusters find evidence for
hot metal-rich outflows preferentially aligned with the large-scale axes of
X-ray cavities with typical outflow masses of around $10^{9} $ - $10^{10}
M_{\odot}$. Here we perform a suite of three hydrodynamic simulations to
investigate whether AGN jets could drive these metal-rich outflows in a
representative cluster. By using both the tracer variable and virtual particle
methods, and additionally following the gas metallicity evolution, we show that
metal-rich gas initially located in central regions can indeed be uplifted by
the AGN bubble to large distances, a phenomenon called Darwin drift in fluid
mechanics, and forming a filamentary trailing outflow extending beyond $100$
kpc behind the bubble. The gas entrained in the trailing outflow is entirely
outflowing with an average outflow rate of nearly $100M_{\odot}$/yr during the
first $100$ Myr, and at later times, a growing lower part flows back towards
the cluster center due to gravity. The outflow mass rises up to about $10^{10}
M_{\odot}$ with entrained iron mass of about $10^{6} - 10^{7}M_{\odot}$,
consistent with observations and predictions from the drift model. By the end
of our simulation ($\sim 800$ Myr after the AGN event), several
$10^{9}M_{\odot}$ of the uplifted high-metallicity gas still remains at large
altitudes, potentially contributing to the enrichment of the bulk ICM and the
broadening of central metallicity peaks observed in cool core clusters.
