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

• Main Authors: Eljaouahiry A., Arfaoui A., Assoul M., Aniss S.
• Format: Article
• Language: English
• Published: EDP Sciences 2019-01-01
• Series: MATEC Web of Conferences
• Subjects: Interfacial instability; quasi-periodic oscillation; Floquet’s theory.
• Online Access: https://www.matec-conferences.org/articles/matecconf/pdf/2019/35/matecconf_cmm18_07011.pdf

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.