Interfacial instability of two inviscid fluid layers under quasi-periodic oscillations

Abstract

We investigate the effect of horizontal quasi-periodic oscillations on the stability of two immiscible fluids of different densities. The two fluid layers are confined in a cavity of infinite extension in the horizontal directions. We show in the inviscid theory that the linear stability analysis leads to the quasi-periodic Mathieu equation, with damping, which describes the evolution of the interfacial amplitude. Thus, we examine the effect of horizontal quasi-periodic vibration, with two incommensurate frequencies, on the stability of the interface. The numerical study shows the existence of two types of instability: the Kelvin-Helmholtz instability and the quasi-periodic resonances. The numerical results show also that an increase of the frequency ratio has a distabilizing effect on the Kelvin-Helmholtz instability and curves converge towards those of the periodic case.

Keywords

• Interfacial instability
• quasi-periodic oscillation
• Floquet’s theory.