Rayleigh–Taylor instability subjected to dual-frequency normal vibration

In this paper, the Rayleigh–Taylor instability (RTI) subjected to a dual-frequency vibration in the normal direction of the viscous interface is studied theoretically. In comparison to the case with single frequency vibration, an enhanced suppression effect on RTI is achieved due to the coupling effect between the low-frequency vibrations. When the vibration frequencies are high, however, the vibration amplitude required to stabilize the interface or the neutral vibration amplitude becomes nearly independent of the phase lag between the vibrations, and the enhanced suppression effect diminishes. This phenomenon is explained by an asymptotic analytical solution of the neutral vibration amplitude at high-frequency limit, where the influences of viscosity and vibration phase lag can be ignored, and the suppression effect of the dual-frequency vibrations is equivalent to that of a single frequency vibration with an effective frequency. In addition, the enhanced suppression effect on RTI is weakened at high Ohnesorge numbers but is maximized at a low but finite Ohnesorge number with a specific mixing angle, indicating that the viscous force, the surface tension, and the frequency coupling are necessary for an optimal suppression of RTI with multi-frequency vibrations.