Cubic nonlinear analysis of interaction between a surface wave and two interfacial waves in an open two-layer fluid

Abstract

A third-order asymptotic analysis is conducted to study the three-dimensional resonant interaction between a monochromatic progressive surface wave and two oblique interfacial waves in an open, lightly viscous, two-layer fluid of intermediate depth. By solving the evolution equations of the waves, the short- and long-term behaviors of the interfacial waves are studied. The analysis provides a correction to the second-order theory. The results indicate that the third-order analysis predicts a much lower limit on the growth of the interfacial waves than the second-order theory. Furthermore, in the long term, viscous effects cause the interfacial wave amplitudes to approach a constant value. The effects of viscosity, surface wave frequency, surface wave amplitude, density difference of the layers and relative thickness of the two layers on the dynamics of the waves are examined. The theory is in qualitative agreement with laboratory observations.