Instability of a viscous interface under horizontal quasi-periodic oscillation

Abstract

We study the linear stability of two superposed layers of viscous, immiscible fluids of different densities. The whole system is subject to horizontal quasi-periodic oscillation with two incommensurates frequencies ω1 and ω2. The spectral method and Floquet’s theory combined with Runge-Kutta method are used to solve numericelly the linear problem. We analyse the influence of the frequencies ratioω=ω2ω1$ \omega = {{{\omega _1}} \over {{\omega _2}}} $, on the mariginal stability. The numerical solution shows that the quasi-periodic excitation has a stabilizing or a destabilizing effect on the Kelvin-Helmholtz instability as well as in the parametric resonances depending on the frequency ratio and the amplitudes ratio α=α2α1$ \alpha = {{{\alpha _2}} \over {{\alpha _1}}} $.

Keywords

• Linear stability
• quasi-periodic oscillation
• Runge-Kutta
• Floquet’s theory
• instability of Kelvin-Helmholtz
• parametric resonance.