A REDUCED MODEL FOR INTERNAL WAVES INTERACTING WITH SUBMARINE STRUCTURES AT INTERMEDIATE DEPTH
Internal waves | inhomogeneous media | asymptotic theory
A reduced one-dimensional strongly nonlinear 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 depth of the bottom region is comparable to the characteristic wavelength. The nonlinear evolution equations obtained describe the behaviour of the internal wave elevation and mean upper-velocity for this water configuration. The system is a generalization of the one proposed by Choi and Camassa for the flat bottom case in the same physical settings. Due to the presence of topography a variable coefficient accompanies each space derivative. These Boussinesq-type equations contain the Intermediate Long Wave (ILW) equation and the Benjamin-Ono (BO) equation when restricted to the unidirectional wave regime. We intend to use this model to study the interaction of waves with the bottom profile. The dynamics include wave scattering, dispersion 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.