Analytical and Experimental Investigation of Nonlinear Resonant Interaction between Surface Wave and Interfacial Waves

Nonlinear resonant interaction between surface waves and especially surface waves with interfacial waves is a powerful mechanism for causing instabilities by increasing interfacialwave’s amplitude in special resonant conditions. In case of resonant interaction between surface wave and interfacial waves, Most of previous researches include nonlinear resonant interaction in 2nd order analytical solution by calculating initial growth rate of interfacial waves amplitude.Laboratory observations have been shown when interfacial waves reach to maximum amplitude with a constant exponential growth rate, the increasing stop and the amplitude approach to finalconstant amplitude oscillatory. The 2nd order perturbation analysis can not model the physicalbehavior of long time interaction. In present paper, the 3rd order perturbation analysis was used for obtaining resonant coefficients. For modeling the diffuse layer thickness, a new model hasbeen presented which can consider the change of diffuse layer thickness from zero to maximumas a second order function of interfacial wave amplitude. The results show that 3rd order analysis with new diffuse layer model can predict the physical behavior of long time resonant appropriate

Keywords:

interfacial waves , surface wave , resonant interaction , nonlinear effects , two-layer fluid