The derivation of an isotropic model for internal waves and its application to wave generation

In contrast to two-dimensional oceanic internal waves which have been extensively investigated, there are relatively few theoretical studies on three-dimensional internal waves. The most remarkable theory describing three-dimensional internal waves is the Kadomtsev-Petviashvili (KP) equation. Nevertheless, two shortcomings - unidirectional propagation and anisotropy - limit its application in some general cases. In the current paper, via an asymptotic analysis, we derive an isotropic and bidirectional model, the modified Benney-Luke equation, for a two-layer fluid with bottom topography which can vary both in time and space, therefore tides and currents can be incorporated into the internal wave problem due to the relative motion. In the derivation, the assumption of incompressibility and long waves are invoked and the effects of the Earth's rotation and dissipation are ignored. Based on this model, the generation of nonlinear internal waves by background currents and barotropic tides flowing over topography are investigated. The resulting equation aims to facilitate dynamical analyses, as well as the interpretation of in-situ observational data and laboratory experimental results