A two-dimensional, depth-integrated model for internal wave propagation over variable bathymetry

Based on assumptions of an inviscid fluid and weakly rotational flow, a set of depth-averaged governing equations are developed to model long internal waves in two horizontal dimensions. These waves are assumed to be weakly nonlinear and weakly dispersive, existing in a two-layer system with a small density difference between the layers. No restriction is placed on the bathymetry or the dominant wave propagation direction. A high-order, finite difference numerical algorithm is developed, formally accurate to (Δx) ⁴ in space and (Δt) ⁴ in time. The model is checked with known analytical solutions and experimental data. Real bathymetry case studies are also performed, including simulations of internal waves evolving in the Strait of Gibraltar and near the island of Dongsha in the China Sea. Numerical results show strong similarities to satellite images taken over the same locations.