Abstract
The evolution of small initial perturbations is investigated in a system consisting of a heavy layer of a Newtonian viscous fluid covering a half-space of an ideal fluid with another density. The entire system can move as a rigid entity in the vertical direction according to some prescribed law. By using the apparatus of linearization of the equations and the boundary conditions, the characteristic equation is derived and the high-viscosity limit, in which the two parameters determining the stability are the thinning and the overload, is treated analytically.
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