Linear stability analysis of two fluid columns of different densities and viscosities subject to gravity

We investigate the linear stability of a vertical interface between two fluid columns of different densities and viscosities under the influence of gravity. This work continues from the inviscid analysis presented last year, which showed that the interface was unconditionally unstable at all wave modes, despite the presence of surface tension, and that instability grew as the exponential of a quadratic function of time. Currently, we initially employ the quasi-static approach based on frozen approximation of the base flow and solve the eigenvalue problem. The eigenmodes then act as initial conditions for the initial value problem of the time-dependent base flow. Preliminary results indicate that perturbations: i) grow as the exponential of quadratic function of time at small wavenumbers; ii) grow with rate less than that of i) as wavenumbers increase; iii) decay at large wavenumbers as viscous effects become dominant; iv) are neutrally stable at lower wavenumbers than predicted by eigenvalue analysis. Results will be compared to the asymptotic solutions for validation. The role of varying Reynolds number, density and viscosity ratios will be presented.