Boussinesq equations for internal waves in a two-fluid system with a rigid lid

A theoretical study of Boussinesq equations (BEs) for internal waves propagating in a two-fluid system is presented in this paper. The two-fluid system is assumed to be bounded by two rigid plates. A set of three equations is firstly derived which has three main unknowns, the interfacial displacement and two velocity potentials at arbitrary elevations for upper and lower fluids, respectively. The determination of the optimal BEs requires a solution of depth parameters which can be uniquely solved by applying the Padé approximation to dispersion relation. Some wave properties predicted by the optimal BEs are examined. The optimal model not only increases the applicable range of traditional BEs but also provides a novel aspect of internal wave studies.