  We investigate the influence of rotation on the onset and saturation of the
Faraday instability in a vertically oscillating two-layer miscible fluid using
a theoretical model and direct numerical simulations (DNS). Our analytical
approach utilizes the Floquet analysis to solve a set of the Mathieu equations
obtained from the linear stability analysis. The solution of the Mathieu
equations comprises stable and harmonic, and sub-harmonic unstable regions in a
three-dimensional stability diagram. We find that the Coriolis force stabilizes
the flow and delays the onset of the sub-harmonic instability responsible for
turbulent mixing at lower forcing amplitudes. However, at higher forcing
amplitudes, the flow is energetic enough to mitigate the stabilizing effect of
rotation, and the evolution of the turbulent mixing zone is similar in both
rotating and non-rotating environments. These results are corroborated by DNS
at different Coriolis frequencies and forcing amplitudes. We also observe that
for $\left(f/\omega\right)^2<0.25$, where $f$ is the Coriolis frequency, and
$\omega$ is the forcing frequency, the instability, and the turbulent mixing
zone size-$L$ saturates. When $\left(f/\omega\right)^2\geq0.25$, the turbulent
mixing zone size-$L$ never saturates and continues to grow.
