Analysis of propagation of weakly nonlinear waves in a two-layer fluid with free surface

Abstract

The study of wave motions in stratified fluids is one of the main tasks of hydrodynamics, which is caused by both theoretical and practical needs. Analytical analysis of propagation of weakly nonlinear wave packets in a two-layer fluid of finite depth in the presence of a free surface is performed. As a result, evolution equations of wave packets on the interface and the free surface in the form of the second-order nonlinear differential Schrodinger-type equations were derived. The form of internal and surface waves depending on the ratio of layer densities and the wave number considering the surface tension was analyzed. As a result, the effects of taking into account the second approximation in modeling wave motions in the two-layer system, which leads to blunting or sharpening of the wave crests and troughs were revealed. The analytical results are confirmed by field observations.