Abstract
<title>Abstract</title> <p>Internal waves in stratified oceans are generated by both direct mechanical forcing from moving bodies and nonlinear resonant wave–wave interactions. While moving bodies provide localized energy input, resonant interactions redistribute this energy across the internal wave spectrum, coupling external forcing with the intrinsic nonlinear dynamics of the wave field. Motivated by experimental observations and field studies, we investigate the effect of a density gradient layer on the resonant generation of internal waves by a surface wave theoretically. The fluid system is modeled as a combination of two homogenous finite-depth layers, divided by a thin intermediate layer. We use a variational formulation of the weakly nonlinear interaction couple with the averaged Lagrangian concept to shorten the complex calculations and derive closed-form expressions for the growth rates of the internal waves. The results show that the internal waves have shorter wavelength but higher chance to grow when there is a transition layer between the surface and the denser layer. The highest growth rate of the internal waves occurs when these waves travel almost normal to the surface wave direction. Previous experimental measurements support the theoretical findings.</p>