Progress in internal wave theory for two-layer and three-layer fluid systems

Internal waves, occurring in stratified ocean, are ubiquitous in the world oceans. It is of great significance for our country′s marine development to study the generation and evolution of internal waves. Based on the internal wave theory of two-layer and three-layer fluid systems, the KdV (Korteweg-de Vries) internal wave theory, MCC (Miyata-Choi-Camassa) internal wave theory, HLGN (high-level Green-Naghdi) internal wave theory and Dubreil-Jacotin-Long internal wave theory, which were widely used at home and abroad, were selected to review their research progress. The advantages and limitations of different internal wave theories were discussed from mathematical models, theoretical research and numerical simulations. In the view of mathematical derivation, it is proved that MCC internal wave theory is equivalent to the first-level HLGN internal wave theory.