Hydrodynamic characteristics of a vertical thin barrier in a continuously stratified fluid

This paper discusses the interaction of water waves with a verticalthin barrier in a continuously stratified fluid. Under the Boussinesqapproximation, the dispersion relations are obtained for planemonochromatic waves in a continuously stratified fluid, and the theoreticalsolutions are obtained by the eigenfunction expansion for the reflectionand transmission energies, as well as the exciting forces on the barrier dueto incident waves. For a fixed frequency \omega , when \omega >N(N being the buoyancy frequency), there is only a monochromatic wavepattern with one mode. When \omega < N, there are monochromatic wavepatterns with infinite modes, and it is shown that for the incident wave ofeach mode, the energies of the reflection and transmission waves of anyother mode are equal. The reflection and transmission energies, as well asthe exciting forces on the barrier due to incident waves are computed fortwo types of structures: a surface-piercing barrier and abottom-touched one, respectively. The results indicate that the densitystratification can have a significant effect on the hydrodynamic characteristicsof the barrier over a wide range of frequencies. In particular, when \omega< N, the transferred energies and the exciting forces on the barrier due toincident waves of the first mode are much less than those due to incidentwaves of other modes.