Wave transformation by a vertical barrier between a single-layer fluid and a two-layer fluid

The reflection and transmission of water waves by a vertical barrier between a homogeneous fluid and a two-layer fluid are investigated for two different types of barrier: type I is a surface-piercing barrier and type II a bottom-standing barrier. For a type I barrier, the lower-layer fluid is the same as the homogeneous fluid and has a higher density than that of the upper-layer fluid. For a type II barrier, the upper layer fluid is the same as the homogeneous fluid and has a lower density than that of the lower-layer fluid. For any given finite thickness of the fluid layers, a hydrostatic equilibrium state exists. Incident progressive waves can then be transmitted through the gap beneath or above the barrier. By using the linear wave theory and eigenfunction expansions, these boundary value problems are solved by a suitable application of the least-squares method. The definitions of the corresponding reflection and transmission coefficients art: introduced in each case. For the two-layer fluid, there are two different wave modes: the surface (barotropic) and interfacial (baroclinic) wave modes. It is found that water waves, propagating either fi om the homogeneous or from the two-layer fluid, are partially reflected or transmitted and produce simultaneously both modes of water waves in the two-layer fluid.