Preliminary study on higher-order modified Boussinesq equations for internal waves in a two-fluid system

This paper performs a preliminary examination for higher-order modified Boussinesq equations for internal waves propagating between a two-fluid system bounded by two rigid walls. A set of three equations constitutes the new equations in which two dpeth parameters denoting two arbitrary elevations make the model flexible. To acquire the optimal model, the technique of Padé approximation is used to compare the linear wave theory and present model to determine two depth parameters. Dispersion relations predicted by present model and previous models are analyzed. The main goal of present study is to provide a theoretical foundation for further numerical simulations.