Transformation of water-wave energy in two-layer ocean in the presence of surface tension

In the present paper, transformation of water-wave energy in a two-layer fluid having irregular bottom is studied including the effect of the surface tension. In such fluid system, time harmonic waves of two distinct modes (wave numbers) exist. When an incident wave with a particular wave number encounters the irregular bottom, it is partially reflected as well as partially transmitted into waves of both wave numbers. As a result, some of the energy is transferred from one to another wave number. Perturbation analysis followed by Fourier transformation is used to study the reflection and transmission phenomena. Reflection and transmission coefficients of both modes are estimated up to the first-order. These coefficients are obtained in integral forms and depend on the bottom profile. One special type of shape function is considered to evaluate the related coefficients. These coefficients are shown in graphical forms to demonstrate the effects of some physical parameters like number of ripples, surface tension on the transformation of wave energy between the waves of two different modes. Moreover, a comparison has been made between the present results and the experimental results available in the literature.