  Hydrodynamic instability of a gravity-driven flow down an inclined plane is
investigated in the presence of a floating elastic plate which rests on the top
surface of the flow. Linear instability of the system with respect to
infinitesimal disturbances is captured using normal-mode analysis. The critical
conditions for instability are obtained analytically utilizing the long-wave
approximation and small film aspect ratio. Further, the bifurcation of the
nonlinear evolution equation is analyzed using weakly nonlinear stability
analysis. The Orr-Sommerfeld system for the perturbed flow is derived, and it
is solved numerically using the spectral collocation method. The behaviour of
the marginal stability curves and temporal growth of the unstable waves are
portrayed for a range of dimensionless flow parameters. Moreover, the pressure
acting on the surface and shearing stress are calculated and analysed for
various structural and flow configurations. The study reveals that critical
structural parameters such as rigidity and mass per unit length play a crucial
role in suppressing and facilitating the unstable surface waves of the flow.
Numerical observations imply that the floating elastic plate helps to stabilize
the surface flow and to damp the high amplitude waves.
