Internal and Surface Waves in a Two-Layer Fluid
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In order to investigate the validity of the rigid-lid approximation, two fluid systems, a free-surface system and a rigid-lid system, are compared. Both the free-surface and rigid-lid systems have waves propagating at the interface between two layers of immiscible fluids of different densities, a deep bottom with featureless topography and a surface boundary. The surface boundary of the free-surface system is considered free, whereas the surface boundary of the rigid-lid system is a rigid-lid. The full (Euler) models for these situations are reduced to systems of linear evolutionary equations posed spatially on two dimensional Euclidean space. Compatible initial-boundary-valued problems for these systems of equations are compared in order to obtain sharp estimates of upper fluid layer depths and time scales over which the rigid-lid approximation is valid.