Instability mechanism of shear-layered fluid in the presence of a floating elastic plate

In this study, linear stability analysis in the two-dimensional Cartesian coordinate system is used to analyze the flow dynamics underneath a large floating elastic plate over a slippery surface in the presence of external shear. For both viscous and inviscid flows, the Orr-Sommerfeld equation and the Rayleigh equation, respectively, are obtained using normal mode analysis. The Chebyshev collocation method is used to solve both equations numerically. Analysis of the growth rate and energy distributions is performed to understand the flow instability at various flow and structural parameters. The study reveals that the flow below the floating elastic plate dampens for larger uniform mass and structural rigidity in the viscous fluid. On the other hand, there is no effect of structural rigidity on the flow stability in the case of inviscid flow. However, the plate of larger uniform mass stabilizes the growing disturbance generated due to the externally imposed shear at the surface of the plate. The present study is analogous to the simple geographical model of external shearing on the surface of a large ice cover zone caused by atmospheric air. This study can be extended to understand the flow stability below other large floating structures like a floating island and a floating airport.