Hydrodynamic stability analysis of shear-layered fluid flow over a porous bed in the presence of a floating elastic plate

The present research investigates the stability characteristics of external shear-driven horizontal fluid flows over a porous horizontal plane in the presence of a floating elastic plate. A two-domain approach is considered to describe the model. The study employs the Chebyshev spectral collocation method to generate and solve the Orr-Sommerfeld eigenvalue system numerically. The most unstable mode is detected through eigenspectrum in finite wavenumber region. The plate characteristic parameters contribute to stabilizing the surface wave instability by reducing the linear wave speed and perturbed growth rate, but compressive force follows the other way. However, the external shear has the potential to enhance the surface wave instability by increasing the bulk velocity of the fluid. The depth ratio between the fluid and porous layer and Darcy number shows a dual nature regarding stability. So, by selecting specific characteristic parameters for both the flexible plate and porous bed, it is possible to manage and control the instability of the shear-layered film flow.