The onset and saturation of the Faraday instability in miscible fluids in a rotating environment

Abstract

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 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 subharmonic unstable regions in a three-dimensional stability diagram. We find that the Coriolis force delays the onset of the subharmonic instability responsible for the growth of the mixing zone size at lower forcing amplitudes. However, at higher forcing amplitudes, the flow is energetic enough to mitigate the instability delaying effect of rotation, and the evolution of the mixing zone size 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$(\,f/\omega )^2<0.25$, where$f$is the Coriolis frequency, and$\omega$is the forcing frequency, the instability and the turbulent mixing zone size-$L$saturates. When$(\,f/\omega )^2\geq 0.25$, the turbulent mixing zone size-$L$never saturates and continues to grow.