The stability of flow over an elastic boundary

Experiments with printing presses show unusual behavior when a fluid flows between rubber and rigid roller. For better understanding of this behavior, three problems which address the stability near fluid interfaces are considered. First, the stability of a viscous flow between a rigid boundary and an elastic layer is studied. Of particular interest are cases with large Froude number modeling rotational effect, and cases with an elastic layer thin as compared to the depth of the fluid. Linear stability is considered using a spectral method. Second, the inviscid flow between a rigid boundary and an elastic layer is studied. Two fluid layers are considered to model boundary flow near the elastic layer. The parameters of interest are the fluid velocity ratio and the fluid depth ratio. Linear stability is considered and an analytical solution is found. The final problem is the study of vicious shear flow with a free surface. Again, a linear stability is considered using a spectral method