Instability of a viscous interface under horizontal quasi-periodic oscillation

University of Hassan II, Faculty of Sciences Aïn-Chock, Laboratory of Mechanic, B.P. 5366 Maarif, Casablanca, Morocco.

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 ratio$\omega =\frac{{\omega }_2}{{\omega }_1}$, 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 $\alpha =\frac{{\alpha }_2}{{\alpha }_1}$.