On 1:2 resonant waves which arise between two stratified fluids of finite vertical extent in the presence of mean flow effects

A study is made of the profiles which arise on the interface of two fluids of different densities and which arise from the interaction of the first and second harmonics of the motion. The fluids are constrained above and below by impermeable plates and are subjected to the twin restoring forces of gravity and surface tension. The method of multiple scales in both space and time is employed to derive a system of coupled nonlinear partial differential equations which models the evolution of the interface. In addition, an examination of the stability of the interface profiles was undertaken. A fairly simple stability criterion was found and the waves were shown to be highly stable. These results therefore provide encouragement to experimentalists who might be able to generate these waves in the laboratory.