Preprint E7/2007
A REDUCED MODEL FOR INTERNAL WAVES INTERACTING WITH SUBMARINE STRUCTURES AT GREAT DEPTH
André Nachbin | Ruiz de Zárate, Ailín
Keywords: Internal waves | inhomogeneous media | asymptotic theory
A reduced one-dimensional model for the evolution of internal waves over an arbitrary bottom topography is derived. The reduced model is aimed at obtaining an efficient numerical method for the two-dimensional problem. Two layers containing inviscid, immiscible, irrotational fluids of different densities are defined. The upper layer is shallow compared with the characteristic wavelength at the interface of the two-fluid system, while the bottom region is deeper. The non-linear evolution equations describe the behaviour of the internal wave elevation and mean upper-velocity for this water configuration. These Boussinesq-type equations contain the Intermediate Long Wave (ILW) and the Benjamin-Ono (BO) equations in the unidirectional wave regime. We intend to use this model to study the interaction of the wave with the bottom profile. The dynamics include wave dispersion, reflection and attenuation among other phenomena. The research is relevant in oil recovery in deep ocean waters, where salt concentration and differences in temperature generate stratification in such a way that internal waves can affect offshore operations and submerged structures.